As someone who grew up in a very cold weather environment, I can tolerate the cold better than almost anyone but as soon as it gets above 50 it's shorts and t shirt weather for me. The slightest bit of heat can cause me to sweat a LOT and I'm one of those people who keeps their apartment as cold as possible all year round.
Given this background info, you can get how I would be flabbergasted on how people in like the 1800s weren't constantly sweating - they always wore long pants, long dresses, long sleeves and (in the case of upper class folks) various suit jackets. Not to mention the complete lack of indoor air conditioning until relatively recently, and if you go even further back, water wasn't always readily available and safe to drink.
So my question is the following - how on earth did people survive summers dressed so conservatively and with little access to water? Were their bodies just used to it? Did having less salt in their food make them sweat less and less dehydrated? Or did people actually wear looser and more comfortable clothing outside back in the day but it's never been really portrayed in film?
and if you go even further back, water wasn't always readily available and safe to drink.
Untrue. This is a myth, and people have had reasonable access to water for the entirety of human history. Remember, humans need water, and humans have not had water treatment for all that long - which means that natural water sources were sufficient for human use for the vast majority of history. While my usual post focuses on the Middle Ages, the hydrology remains the same the world over. Water is safer than you think, else we'd all have died of dehydration already. Remember, kids! Dehydration kills within days!
For the clothing end of things, I commend you to this collection of answers from u/mimicofmodes, u/colevintage, and u/kittydentures.
One more note: I notice you've said that you grew up in the cold, and thus can tolerate it better. On my end, I grew up in the heat. Temperature over here hovers around 30 C (86 F, if you really must); the weekly forecast has a highest temp of 33 C (91 F) and a lowest temp of 26 C (78 F). I consider it time to bundle up and dress warm if the temperature dips below 25 C.
Put another way: You get used to it. Especially if you grew up with it.
Housing was built differently for one.
Where I live, traditionally a style of housing that was built was called a "Queenslander".
https://www.househistories.org/qld-house-designs-1887-1920
Queenslanders were built on stumps, allowing for airflow underneath. (And also some flood protection)
They had verandahs, most wrapping around the majority if not all of the house. This prevented direct sunlight from entering in the house.
Multiple rooms would have doors and many windows, allowing even more air into the house.
On top of this the verandahs usually where screened in, and sometimes got converted into bedrooms, called 'sleep outs' which meant you could sleep outside in the cooler weather. (One of the hardest parts of the heat can be getting to sleep!)
Most rooms would have ceiling fans and ceiling roses.
Then, post war, housing changed for a few reasons, including access to materials and needing to bud houses quickly and more affordably..
However, these days Queenslanders can seem more hot than other housing, due to a lack of installation which can mean they are harder to cool with air-con etc.
A lot of renovations over the years have completely closed in verandahs, taking away the cooling effect (and leaving some really janky floorplan)
People also knew how to dress for the weather, just not in the way we do today.
Neal Hurst's "for the heat is beyond your conception" details how Euro-Americans used lightweight textiles to make summer versions of all the long/covering garments you referenced in the OP, or modified existing garment patterns and construction methods to make them more suitable to the heat, such as wearing coats made from a single layer of unlined linen. These garments also have the advantage of being much easier to launder than the woolens typically used in European outerwear, so if you sweat, it's at least easier to wash it out.
It's worth considering how people dress to this day in desert environments. They don't usually wear shorts and T shirts, they wear single layer lightweight clothing that covers almost their entire body to protect them from the sun. The garments described by Hurst do the same thing.
Finally, go look up Thomas Jefferson's temperature recordings of Williamsburg Virginia in the 1770s. Average summer temperatures are somewhat hotter today than they were in the 17th/18th centuries, which are part of a period often referred to as "the little ice age" by historians and climate experts.