The "Otter" here is Ohthere (Old English), a Norwegian who'd described travels that he relayed to king Alfred the Great in a manuscript that's from Alfred's time (the 800s). "Othere" is the Old English rendering of the Old Norse name Óttarr. This the only account of Bjarmia in Old English sources and one of few sources that give insight into Norse geography that's from the Viking Age. (800-1100) He describes the Beormas living to the northeast of Norway, beyond the Finnas - meaning Sámi here. (see e.g. this recent comment of mine on who the Old Norse 'finns' were)

Othere was writing from a Norse perspective. Later sources, from the Scandinavian Middle Ages (1100-1550) include a few Latin sources (e.g. Gesta Danorum) but most mentions are in Old Norse and found in the Saga literature of Iceland, mostly from the 13th and 14th centuries.

So already there, we have a fundamental problem about the Bjarmians: It's framed entirely from the Old Norse (outside) perspective. Merely because they called some group of people "Bjarmians" does not mean that group called itself something like that, or even that that group of people even considered themselves to be a single people. For instance the Slavic peoples of the Baltic region were consistently referred to as Vindar/Vendar ('wends') even though they didn't consider themselves a single people. It was used of the people in Pomerania in North Germany; it was used of the people in today's Russia (and is in fact the origin of the Finnish word Venäja for Russia)

That Othere's Beormas in Old English are the same people as the Old Norse Bjarmar recorded later isn't in doubt though; the location and pronunciations are essentially the same. Othere's account is as follows:

Then a large river there stretched up into the land. Then they turned up into that river, because they dared not sail on past [or across] the river because of hostility, since the land was all settled on the other side of the river. He had not previously encountered any settled land since he travelled from his own home, but there was waste land all the way on his starboard side, except for fishermen and [wild]fowlers and hunters, and they were all Finnas, and open sea was always on his port side.

The Beormas had settled their land very well, but they dared not come in there. But the land of the Terfinnas was all waste, except where hunters camped, or fishermen, or fowlers. The Beormas told them [or him] many stories both about their own land and about the lands that were around them, but he did not know what there was of truth in it, because he did not see it himself. The Finnas and the Beormas, it seemed to him, spoke practically one and the same language.

So, Othere makes two points clear: The Bjarmians are settled people who engage in agriculture, as opposed to the Finnas, and he seems to think the language was similar. That's not really enough to say whether it was a different Sámi group, or a Finnic group. Or even something else.

Othere's account is, compared to the others, the most primary of sources, though - nearly straight to the page from an eyewitness. Later sources are much more problematic.

In the 1100s you have Saxo Grammatius' Gesta Danorum, where the Bjarmians figure briefly in a few legends, where they (among other things) repeatedly conjure bad weather, destroying Norsemen's ships. They speak of Bjarmian kings, but also Sámi kings; which we know were not really a thing.

Likewise the late 12th century Historia Norwegiae has this to say at the start:

However, towards the north there are, alas, a great many tribes who have spread across Norway from the east and who are in thrall to paganism. That is, the Kirjalers and Kvens, the Horned Finns, and two kinds of Bjarms (Bjarmones). Yet we know nothing for sure of the races that dwell beyond these. Nevertheless after some sailors had tried hard to voyage back from Iceland to Norway but had been buffeted by adverse gales into the Arctic sphere, they finally put in among Greenlanders and Bjarms, where, they claimed, they came upon a people of extraordinary size, and a land of maidens, who are reputed to have conceived when they have sipped water.

This idea of amazon women in the north likely comes from Adam of Bremen, who wrote of such a thing a century before. That, in turn has been suggested to possibly be a misinterpretation of the name Kvenland as being from Kvenna-land ('land of women'). In HN the land of these amazon women and Kvenland are not identified with each other though. (and the identity of the Kvens is also very disputed)

Later sources get increasingly muddled in general; the Icelandic Saga of Saint Olaf, written in Heimskringla, recorded in the 13th century, tells of a Norse raid against a sacred mound of the Bjarmians, full of valuables and with a wooden idol of their god Jómali. The name is pretty obviously derived from the Finnic words for 'god'' (jumala), but the question is whether this can be taken to be accurate for the Bjarmians.

The aspects of pagan cult described are a better match for Norse paganism than what we know of Sámi and Finnic customs. Earlier in the same Saga, we have Finns-in-Finland performing weather magic. The even later Bósa Saga - which illustrates how these stories change as well as anything - repeats another version where the god's name is the same, but the god is now in a temple. (even farther removed from Sámi and Finnic practices)

The story in Heimskringla is based off earlier legends of Saint Olaf that only make passing mentions of this expedition. So the detail of the god Jómali may rather reflect that Heimskringla author Snorri Sturluson believed the Bjarmians to be Finns and fleshed out the story with their god name. On the other hand there are two stories in Heimskringla (Saint Olaf and Ynglinga Saga) that feature Finns-from-Finland and neither has a single word, personal- or place-name that's Finnic. It's all Old Norse names.

The first map with Bjarmaland/Biarmia on it is the Olaus Magnus map Carta Marina from 1539. Olaus did not know of the Icelandic Sagas or Othere's account; it seems based entirely off Saxo's account, which we know he knew of.

Anyway.. rather than list all the sources and historiography, there's an excellent thesis available here - Bjarmaland, by Mervi Koskela Vasaru, which collects all the relevant passages from all the sources and translations of them to English in one place, and also provides an overview of the historiography.

To be clear though; it's hardly likely there was a Bjarmian 'kingdom' in the medieval sense of what a kingdom entails. Nor did Viking Age Scandinavians have that, except perhaps towards the end. The Old Norse term konungr means 'king' but was used for rulers that'd really be considered "chieftains", "warlords" or "petty kings". It does not necessarily imply a consolidated state or any meaningful amount of government beyond the despot himself. Bjarmian kings, much like Sámi 'kings', Finnish 'kings' and for that matter most Norse 'kings'.

As said at the outset, the case of the Bjarmians, we don't know if they were a single people even; we have sources like Historia Norwegiae which divide the Bjarmians into two groups, although without explaining the difference. Finally, Russian/Slavic sources don't mention them at all.