Since time race is the in-game speedrunning mode, shouldn't it be a main category or at least a misc. category as opposed to being in the level leaderboard?

I personally think it's fine as it is. The time categories (all of them, actually) are "non-competitive" (that is to say, the categories themselves receive almost no submissions) as you can tell by easily checking the boards. Most runs are 3-4 years old in medium/hard and easy there was a span of 3 years between recently posted times on easy. It would only bloat the current leaderboard with categories that do see nearly daily/weekly submissions.

I've been a mod probably for 2 - 2.5 years here or something and almost never have seen anyone submit times to time race.

I would argue that the reason time race is non-competitive is because it's tucked away in the level leaderboard. Obviously you're the mod, so it's up to you. But I definitely think it could give that category more prominence, and considering there aren't a lot of categories, I don't think it would bloat the leaderboard too much.

Yes, it would look very bloated: there's already 5 different categories with respective sub-categories, which I personally think it's quite a bit for this game; adding 3 extra categories that will have anyway to be multiplied by 2 due to the regional difference is very honestly not something I'd be willing to consider for now. Besides, every "time race" mode or "time trial" mode, as far as I can recall, it's always represented a secondary game mode by default, so making the "round game" mode the main set of categories I think was the right choice to make when the leaderboard was created, and I think it would make sense to keep it this way. And honestly, I really do believe the individual levels leaderboard is the best way to display the "time race" mode runs: it's one click away from the main leaderboard, the general view displays the fastest runner for each level and there's still associated leaderboards for each difficulty.