Warnings thrown for mkdir despite folder existing

You should take that error at face value, because it is a low-level PHP error. Is the web server process user allowed to create directories there?

I have been, but even setting all folders from files on down to 777 just to test it had no effect. As for the web server process user, this is on ddev, and all the ddev environments (of which this is the only one with the issue) are the same user/group. Could this be an nginx setting, or something to do with .htaccess?

Unless ddev is actually running as a user that maps to a host user, which is unlikely, I think default/files/php needs to be 777 also.

Yes, what I meant was I've tried chmod -R 777 sites/default/files, which made php and php/twig 777, and no joy.

As I said I think default/files/php needs to be 777 also. I could be wrong but AFAICS you did not try that.

That command made
sites/default/files
sites/default/files/php
sites/default/files/php/twig
and all the files in them 777

What command? Did I suggest a command?

FYI the default files permissions in a DDEV install are as follows:

ls -al sites/default/files
total 8
drwxr-xr-x  8 user1  staff  256 Sep  3 13:28 .
drwxr-xr-x  8 user1  staff  256 Sep  3 13:26 ..
-r--r--r--  1 user1  staff  486 Sep  3 13:27 .htaccess
drwxrwxr-x  8 user1  staff  256 Sep  3 13:28 css
drwxrwxr-x  6 user1  staff  192 Sep  3 13:28 js
drwxrwxrwx  3 user1  staff   96 Sep  3 13:27 php
drwxrwxr-x  2 user1  staff   64 Sep  3 13:27 styles
drwxr-xr-x  3 user1  staff   96 Sep  3 13:27 sync

If yours are different, and you are still struggling with this I suggest instead the #support channel in Drupal Slack because I don't feel these comments are helping you.

No, you didn't, I did :-) I just went back (a couple messages up) and formatted it as code.
Ok, I do appreciate your spending the time. This issue seems to be on the cusp of Linux and Drupal...not sure where it will fall. I'll head over to Slack with a pitstop first at ddev.

One other issue could be sluggish syncing between the host and the container. If the host isn't Linux, and it's, for example, Mac OS, be sure that mutagen is running.

So it was weirder weirdness than I thought. It was some docker container glitch. rfay had me clean up docker, power off ddev, turn off mutagen, start it up (messages were gone), power off again, turn on mutagen and start it up, and the messages are still gone.

For anyone who might have the same issue, these were the commands:

ddev poweroff
docker rm -f $(docker ps -aq)
ddev mutagen reset 
ddev config global --performance-mode=none 
ddev start

see if the messages are gone

ddev poweroff && ddev config global --performance-mode=mutagen && ddev start

Resolution: Issue Not Reproducible in Drupal 10.2.3

After further testing, I was unable to reproduce this issue on a site running Drupal version 10.2.3. The warnings related to the mkdir(): Permission Denied error when attempting to create the php/twig folder in sites/default/files are not occurring in this version.

Given that the issue does not persist in 10.2.3, I am marking this issue as resolved and closing it.