In the 264.10-r0 upgrade of elogind, polkit has been disabled in Alpine. This broke tinydm. Thanks for @dylanvanassche for creating a merge request that will fix it: !18965
If you have upgraded to the breaking version, wait until the merge request is merged (should happen any minute now) and new binary packages are built. Then you can upgrade to 264.10-r1, which does not have this problem (either via serial or SSH).
$ sudo apk update
$ sudo apk upgrade
Related: #1000