Update: I think I managed to pinpoint the error. After digging deeper, I noticed the following when running journalctl -b -u rpm-ostreed:
Apr 07 13:48:42 framework-jan rpm-ostree[13995]: Process [pid: 13983 uid: 1000 unit: user@1000.service] connected to transaction progress
Apr 07 13:48:49 framework-jan rpm-ostree[13995]: **
Apr 07 13:48:49 framework-jan rpm-ostree[13995]: OSTree:ERROR:src/libostree/ostree-kernel-args.c:197:split_kernel_args: 'quoted' should be FALSE
Apr 07 13:48:49 framework-jan rpm-ostree[13995]: Bail out! OSTree:ERROR:src/libostree/ostree-kernel-args.c:197:split_kernel_args: 'quoted' should be FALSE
Apr 07 13:48:49 framework-jan systemd[1]: rpm-ostreed.service: Main process exited, code=dumped, status=6/ABRT
Apr 07 13:48:49 framework-jan systemd[1]: rpm-ostreed.service: Failed with result 'core-dump'.
To explain: I had previously added a kernel argument to allow my Framework 11th Gen Intel to suspend correctly. That argument was "acpi_osi=!Windows 2020", changing it to acpi_osi='!Windows 2020' with rpm-ostree kargs --editor seems to stop rpm-ostree from crashing.
Will report back if any issues remain!
Edit: Latest update worked, yay! 