I can't seem to find many anecdotal stories or detailed descriptions of Singapore's POV so I would greatly appreciate it if someone could help me.
As a small, rather urbanized colony, the week-long Battle of Singapore would have been a short, scary, but altogether not unexpected experience for most people in Singapore (I use this over 'citizens' - most would be British subjects, or settlers), who would already have experienced the shrill sirens warning of aircraft raids, observed in newspapers and in word of mouth the Japanese advance down Malaya, and felt the squeeze of wartime extraction and supply shortages under the colonial administration. For many, urban areas were far more dangerous than rural ones, necessitating a high degree of movement, adding to the stream of from peninsular Malaya would have streamed in over the previous month of fighting. All this would have been accompanied with a trepidation of the impending occupation. As you allude to, a large part of Singapore's public history and popular historical memory surrounds the Japanese occupation after the battle, rather than the battle itself. Many histories of battles appear curiously depopulated, despite the fact that street fighting occurred in some residential areas (never fully emptied, even if many had left in anticipation of fighting).
Where the battle is indeed discussed, historiographically most of it revolves around its military actors (e.g the National Library’s writeup), namely the unexpected weakness of the British defence, or select stories of bravery from 'local' soldiers. The latter is more interesting to me to observe, both in terms of the museum/memorial site (debates over its name, the difficulties in identifying and situating the compound on a 'battle site' itself - it now lies in a colonial-era bungalow that would've been used for ammo storage!) as well as the historical identities of its heroes (was Lt. Adnan, the face of the Malay Regiment's 'last stand' "Singaporean" in that sense? Both Singapore and Malaysia have laid claim to him, and he was fighting first and foremost as a colonial subject in the imperial army.) But that's not the focus of your question, and I'll leave that to the excellent discussion of collective memory of WWII by two Singaporean academics.
In thinking about the lived experience of the battle, I’d like to note that such experiences – like those of any battle – were highly differentiated one. Where you lived, what occupation you had, what your family was like, would have mattered significantly. Not many Singaporeans participated in the army – where they did, it was largely in the capacity of Straits Settlements Volunteer Force, receiving light training and play support duties (e.g as ambulance drivers, runners). It sounds like you’re more interested in ‘civilian’ experiences. Here, the National Archives of Singapore has an extensive range of oral history interviews that can be found here. At a quick glance you should be able to pick out a story or two. There are plenty of British/Commonwealth interviewees, although most participated in combat, given that the majority of European women and children would have been evacuated (mostly to Australia) in the leadup to the war.
One trend quickly emerges even within these interviews, however: memories of the battle seem mixed with those of the occupation, suggesting that they were often not discretely periodized (the horrors of war were not readily separable from those of occupation). Of course, there’s room to suggest that some of these came from the framing of the oral history project and the prompting of the interviewers themselves, but even from anecdotal conversations with family members, the chaos of war was also a chaos from the uncertain authority between a British to Japanese transfer of power. True, the British surrender was a temporal marker that many picked up on, as accounts of looting and abandoned posts suggest, but these were in the aftermath of the battle proper.
“ .. Doors, desks, cupboards, safes, and suitcases had been broken open, their content strewn everywhere over piles of empty tins and human ordure: it is a blessing that walls cannot speak or Fullerton Building would never cease from shame. Clothes, shoes, notebooks, diaries, letters, wills, bank books, insurance policies, photographs of loved ones, and all manner of personal articles...lay in utter confusion.” (Corner, quoted in roots.sg)
Rather, for many, their first experience with the battle would have been one of panic, then the announcement over radio of surrender. For Ang Seah San, a civilian member of the Air Raid Precautions team, his first encounter was Japanese troops followed the battle’s official cessation. Asked if he’d encountered any Japanese soldiers fighting, he replied in the negative:
“When their surrender was announced through the radio, we saw them coming from the country to the Serangoon English Schoool. So they were patrolling and before they ceased fire, they baned. I think that’s a signal: for gunshots… that’s the signal for all the other troops that the enemy has surrendered … The feeling was very uncertain. We might have got to go to jail, or put in concentration camps. But the good thing is that we destroyed all the records and we have got no connection with the previous government. We were happy about that.”
An involvement with the colonial government, even in a low administrative capacity, would have placed many at risk, and reading the remainder of the transcript, Ang’s memories of the battle largely involve his civilian life: the domestic, bodily experience of having to share an overcrowded house, anxieties about access to food. For someone previously mobilized during air raids, it’s surprising how little of the combat features in his recollections of the war.
Turning our attention to Middle Road’s hospital, the experience of Ruth Segeram, a Ceylon-born nurse working similarly suggests that being in a hospital made the start of the battle less obvious/ For her, working nearly 24 hours a day when shelling of the island began in earnest, not sleeping for three or four days was the most visceral and difficult part of life in February 1942.
“You didn’t realize that human endeavour could be so… the need was there and we had to do something. There were so few of us because the others couldn’t come … We just kept on because the need was there. We just kept on.”
Her experience of the penultimate day reveals a tense silence.
“There was a stillness. There was no bombing. There was no shelling. All those awful wheezing noises stopped. So we realized that something must have happened.”
So disconnected were the hospital staff from the battle that they actually thought that the Japanese, not the British surrendered! When rumours spread of a Japanese surrender:
“We couldn’t believe it because according to all we have read before, the Japanese never surrender… At that time we realized that the British wouldn’t have given in because they had so many forces here. Anyway the newspaper that came out just before that [likely the Sunday Times]… it was only a tabloid where Sir Shenton Thomas said that Singapore will not fall. It shall not fall. For a long time I had that paper. And so of course we went by, you know we were so accustomed as colonists to believe what was told to us. So we definitely fell… but it was a fortress and everyone knew that. We didn’t realise that it could have been a surrender but it was.”
When they did notice the surrender, it was because “At the last moment quite a number of our European staff just disappeared”, seemingly to be evacuated in the moments before the surrender. Colonial subjects would not have been afforded the privilege of an ignominious goodbye and retreat: the rest of her interview details her troubled life under the occupation.
In the days following, looting, the commandeering of vehicles and property, and soon enough – the infamous ‘Sook Ching’ massacres where Chinese men were detained and executed en masse. Again, that seems to lie outside the scope of your question proper. Nonetheless, the impression we get from many of these interviews is that many civilians did not experience battle directly; if so, the Battle was thought of less as a distinct event in wartime Singapore, and more within a general period of hardship. It was the surrender of the British was a caesura, even a turning point, for many. If anything, writing this answer has made me challenge my initial assumption that the lack of the battle was a historiographical quirk, or an artefact of the postcolonial state’s emphasis on hardship and suffering under the Japanese occupation. What’s surprised me in some part was how disconnected (e.g Ruth) and variegated the experience of battle could be.
Do let me know if you’ve got any more questions!