Since we are still in the very early stages of speedrunning this game, and the run is still very unoptimized so far, I thought I'd share what little documentation I found online on "speedrunning" Me & My Katamari. Most of it will probably be obsolete very soon, if people keep submitting new runs, but for now it could be pretty helpful.
I was surprised how little you can find online on this game, even just basic information about the game. Basically I only found 4 things that could be useful:
1. Low resolution videos of all areas by sloobro (aka slo_bro aka slowbro)
It seems like slo_bro is on of the best M&MK players that can be found online. I watched his videos to find optimized routes for each area before my most recent run, and it helped a lot.
He is also on top of leaderboards you can find on the "Katamari on the web" forum, on which he seems to still be active too (probably on other subforums though).
In the description he talks about speeddemoarchives.org rules, but I couldn't find M&MK on the site, even when I looked at it using the waybackmachine. Most likely because the M&MK community back then mostly kept track of sizes, not times.
2. "Katamari on the web" forum
In the subforum on M&MK are some interesting posts that might be useful at some point. There is one thread in which they discuss how the game decides what area you will be teleported next. If this run should ever be really optimized, finding out how this works is essential. I did not dig further into it so far.
3. Guide "Item List" by slo_bro on GameFAQs
Guide mainly focused on where the find all items (for 100%) with the items sizes. In the beginning theres a small "chapter" on the different areas too.
4. "Me & My Katamari" fandom wiki
Not a lot of useful information here to be honest, but it helped me before my first runs to get some overview of the levels so I'll mentioned it here anyway. Probably better to look at slo_bros guide though.
That's all I got. As I said, some stuff might be useful early on, maybe not a lot, but so far it at least helped me optimizing my routes and cutting off a few minutes of my run.
If anyone has more stuff they found, please share :)