You are starting from an incorrect assumption ... that color management in computers/browsers/OS/players is a constant, uniform "thing" to a set standard.
IT IS NOT.
I am a contributing author for a pro colorist's teaching subscription web service, MixingLight.com. The founders and all of the other authors are based on colorist apps like Resolve, Baselight, and Mistika. The founders were the team hired by Dolby to produce the intense training media for those producing DolbyVision for broadcast/streaming ... these are top colorists.
I produced a program given in the Flanders FSI/MixingLight booth at NAB/2019, and in prep for that spent hours in screen-share and phone calls with Frances Crossman, then color engineer (and now co-product manager for Premiere). At NAB prior to the presentation, I spent a couple hours in person with him. Then before the tutorial for MixingLight was approved for their site, colorists Patrick Inhofer and Robbie Carman participated in a LONG series of intensely detailed emails querying Frances and me. Yea, I've spent some time on this issue.
For pro colorists, there is a massive and continuing discussion concerning the two sides of the same problem: color management for the colorist and for the client/consumer. Especially in this odd time, where they don't do nearly as many client-attended grading sessions as 'normal', where they control the image the client sees. At the current time, clients are viewing via Zoom or one of the several pro tools for such things, oft using various browsers, and of course on gear of un-known color managed controls. It's a big problem.
Most pro video media is still produced 'assuming' the Rec.709 broadcast standards ... sRGB primaries, gamma of 2.4 (sometimes argued for 2.2), 100 nits brightness of the monitor, and produced in a semi-dark room with a highly calibrated an profiled broadcast monitor. This is for broadcast, streaming, and web usage.
But most monitors, even moderately expensive ones that have an included Rec.709 option, do not properly apply Rec.709 standards ... especially the Retina monitors on the Apple system. Browsers ... are all over the place, some sort of applying correct standards, some applying none at all. Players are the same, though VLC and PotPlayer tend to be considered the most reliable.
Settings on the computer, between the OS, user settings for monitors, and settings for the GPU can be all over the place.
All of these crash into each other and create what you are seeing.
So ... how do we navigate all this?
Set your best monitor as tightly as possible to Rec.709 ... use a puck/software combination like preferably the Xrite i1 Display Pro system to set an ICC profile that is strictly sRGB primaries, gamma 2.4, 100 nits brightness, and color with the room in a near-dark state with a bit of lightness on the wall behind the monitor (called bias light) as close as possible to 6,000K.
Then Premiere will give the best results it can, as Premiere is hard-coded to be used on a full broadcast system. Outside of Premiere of course, it's a crap-shoot. Again, VLC/Potplayer are the best options, but some browsers will be close, others not.
And that's all you can do. It's all the pro colorists can do. Grade it on a proper setup, and let it go out Into The Wild.
And understand that out 'there', your media will then look relatively as it should, compared to all other pro produced media on that system. Nothing will ever look the same on another screen besides yours, don't even try.
Here's some other resources ...
Why does my color look different?
FAQ: Setting up for HDR work in Premiere 2020
Why Master On A Calibrated Display?
Color Management for Video Editors
Jarle’s Article on Premiere Color Management
How Do You Finish at the Highest Possible Quality in Premiere Pro CC?
Neil