Hey bro. Not a mod, but I thought I would try to answer you as best I can.

The reason you can't just press 'restart' from the pause menu, is because any time you spend in that match/level IS NOT saved to your 'IN GAME TIME' when you do. In other words, it means that time will not be added to your 'TIME PLAYED' under the 'STATISTICS' page.

If you get a GAME OVER screen before restarting a level/match, then time played in a level IS added to your in-game time.

Since the 'TIME PLAYED' statistic is important to show before/after when running some categories (such as the 100% or full story category), it invalidates the run to press 'restart' from the pause menu, as runners could just keep pressing 'restart' button during their run on levels/matches to get more favourable times for each individual level, and subsequently, the run as a whole.

I'll use an example, if it helps: Lets say you want to run the full story category on hard, but you know that to beat the world record, you need to run Siberia, Chicago, and Notre Dame (and the rest!) in under 3 minutes each. If restarting from the pause menu was allowed, you could just keep pressing restart on the pause menu whenever you got to the end of a level and you realised you ran the level too slow to get the overall world record by the end of the run.

You can see that by pressing 'restart' from the pause menu, it is not a fair reflection of runs and run times, respectively. The rule was brought in so that run times stay legitimate, and are not just purely fabricated from pressing 'restart' 1000 times per level when things aren't/weren't going your way.

So, to summarise, if you want to restart a level, you either have to quit out to the main menu and head back in, or get a GAME OVER screen, as these conditions will save your in-game time accurately and keep your run time valid.

To address your other point... The reason pressing 'restart' from the pause menu on individual level runs (such as Siberia only, or Chicago only) is allowed is because individual level runs are timed with real time, and not the in game timer in the stats menu.

The reason for this is because the only individual level run you can reeeally time with the in-game timer is Siberia, as it is the first on the list and will save your in-game time accurately once you complete the mission and quit. But, this is far from ideal, and it is the reason why most people use an RTA timer such as LiveSplit or Splits when doing individual level runs. Although, having an 'on-screen RTA timer' is actually optional for individual level runs.

Hope this helps you. Always nice to see people still enjoying Timesplitters. It has a lovely cult following tbh.

Happy running!