Thanks to Morris for the extensive analysis:

Definitely Safe Forever

Makes no mention of being worked on by anyone specific, but it's worth noting only James provides commentary.

Snake Escape

James explicitely says "this is one of the best examples on this soundtrack of what Toby and I's respective styles sound like mixed together". Seems to imply this is a Roach arrangement of a Fox composition.

Joey Claire, Extraordinaire

Again, seems to be implied this is a Toby composition, arranged by James.

Half-Harley Manor

Explicitely states the final version is by Toby, seems to have been very collaborative though.

Relatively Visible Darkness

James mentions "Overall it felt like the mansion wasn't dorky enough so I wrote this even MORE toned down version of it for when the lights go out. Stripping down Toby's song" (Half-Harley Manor), seems to imply he did this version himself.

Bedroom for an Annoying Dog

No strong implications on this one, very maybe just by James but idk lmao

That's How I Beat Snake

Weak implications this song is James-only, it's for sure based on a track he wrote, and it doesn't seem like Toby did anything

Jude Harley, Bizarrely

Again, probably just James but no strong indication

Table for Tooth

James exclusively talking in first person, nothing from Toby: most likely just James

Final Spice

(the video linked in the comment is no longer available, though it is archived on the web archive)
This song has a very clear "development cycle". It started as a Toby demo (first instance), which Toby sent to James, who arranged that (second instance) and sent it back to Toby, Toby then rearranged James' version into the final version (third and final instance)

Living Legend

James' commentary seems to imply he was the only one involved on this one.

Singular Peril

implied to be James only, using a Toby sketch as base.

A More Defensible Position

"This is a Toby Track 100%"

Open The Door

seems to be collaborative, but James-skewed. As Toby said: "My main contribution to this track is the piano riff 10 seconds in... Hell yeah..."

Keep Your Head Down

Toby's wording implies he did this one on his own

Oh Whoa, What's This

Toby: "I made this track but I didn't name it. I had nothing to do with the name here. James named this."

Some Kind of Alien

Toby specifically says he made this track, James mentioning "My contribution to this track is that I made Toby go in and add in more tuba." - very specifically Toby-only

Rustblood

sounds like Toby-only

Filthy Nuclear Bunker

"This is the most James Roach™ track on the album"

SPORTS! Personally, I Love Them.

seems to be implying James-only

Lofted Gunpile

commentary implies this is James' take on Some Kind of Alien, which is by Toby. Toby comp., James arr..

SERPENT GENESIS

implied to be James

We Shall Go Together

sounds like the most involvement Toby had on this one is the fact he made Quiet Water from UNDERTALE, which served as inspiration for this song.

Wish You Were Here

again, nothing directly revealing but seems to be just James

Intermission 1

another unavailable video linked, is on web archive
Collaborative, or James-only based involving stuff Toby made

Old Steps

no implications at all

How it Could Have Gone

Toby: "This was basically James's arrangement of MY arrangement"

Alternate Recipe

This is that "second instance" of Final Space that was done by James

Heavy Snaking

James talks in first person, Toby says he doesn't even remember if he heard this song before

SPOOKTUNE

as mentioned in the commentary, this is just a cover of Spooktune James made after Toby showed him the song