https://doc.e.foundation/build-status
No. /e/OS OTA updates on the Fairphone 3/3+ don’t need the recovery at all, because they make use of the A/B device partition layout. Updates get installed in the background on the unused OS slot while you still use the device with the active OS slot, then the necessary reboot just switches the OS slot to the updated OS and has no further work to do than just boot. User data is shared and stays the same.
If you leave the bootloader unlocked, you can boot TWRP with fastboot when you need it. Of course an unlocked bootloader has security implications which need to be considered, but it sure is tempting … Backups, bootloader, root - #5 by AnotherElk.
With an unlocked bootloader, you could even just switch the OS slot with fastboot and boot the older OS version from before the update, but Android rollback protection would demand a factory reset to boot successfully if the older OS version had an older security patch level than the new version, which usually is the case with updates.
You can install TWRP (by embedding it in the boot partition with a script, see twrp.me), but /e/OS updates will restore the original boot partition with the /e/OS recovery, unless you take advanced measures in connection with rooting the phone.
With a locked bootloader you need alternative means for backups.
That sounds like an issue with the initial 1.3-r update on the Fairphone 3/3+ …
… which probably got revoked while developers would check this serious issue, so probably was offered for a while and then was not offered anymore.
https://gitlab.e.foundation/e/backlog/-/issues/5970
Switching the release channel (aka build type) is always a new install.