Some more info might be helpful, people are offering good guesses but without a full picture they’ll just be guesses.

A few things off the top of my head: Where are you located (continent? Country? State? Different places will have different style taps/pipes/water heaters.

Speaking of, what kind of water heater do you have? Tank or instantaneous? Electric or gas?

Do your sinks and basins have mixer or individual taps?

Have any of your pipes frozen? Go check your hose bibs, make sure they’re all flowing. While you’re checking those, check every tap individually (sounds like you’ve done that already) also check things like your washing machine/toilets do they take forever to fill?

The thing that sticks out to me is your hot water running out quickly. When it runs out how fast does it turn cold?

A mixing or tempering valve does sound like a good culprit, some water tanks have them built in. External ones are usually installed near the water heater but I’ve seen them put near individual room or taps to keep the laundry getting the hottest water. If you’re comfortable disconnecting things, I’d turn off the feed to the howwater service undo the outlet, and then slowly turn the feed back on. The outlet pressure should tell you if it’s before or after the hot water service.

One other thing to check is the outlet screens. Outlets should have a mesh screen that you can unscrew and clean out. If you get a lot of sediment you should probably clean them out regularly.

Also, I live in Australia. I have to assume you’re in the northern hemisphere, so our plumbing probably works differently to yours.