why not use in-game time in runs?(source split)

Would that work with save loading? Idk I only run this source game, never ran any others.

yes,the timer pauses when you save and load

Yes, it says in the rules of each category the method of timing.

It runs on an hl2 process so Source Split should work fine. If you want to test it you can set your game to half-life 2 on your splits and activate the Source Split plugin. There is additionally a map whitelist so you could setup for each level properly otherwise it will just do it for every 1 map. If it works fine its possible to get it whitelisted for this game in livesplit.

How should livesplit work, Because the timer starts when you can move, I want livesplit to be paused during the e1m1 loading screen but it won't pause

I have livesplit set up to display ingame time, so that should not be the problem