Good question.
I think you are going to get two to three camps here.

SAVE In File menu for all apps
1) I personally learn 3 decades ago that Ctr + S saves so I do not need to waste space with save button.
2) Others may have been hitting your save button for years.
OPEN In File menu for all apps
1) Many DAWs have a dedicated song browser with tabs. PGM has the Song Tab. 80% of the time I use the OS file browser to go the directories in my organization so no button for me.
2) Others have used your Song Browser.

So, I would vote for let the user decide what buttons are in the tool bar.
You can default you what you have but let others remove them.

Studio One (latest version), Win 11 23H2 , i9 -10940X 3.3 GHz, 32GB Mem, a 4K 40" monitor, PreSonus Studio Live III Console as interface/controller. secondarily test on Reaper, Cakewalk, and S1 on Surface Pro 3 Win 10 (latest versions).