[Google Pixel 3a XL Questions & Answers] sic0048:
Getting an OTA to take while rooted is always hit and miss. I bought this phone in May 2019 and have successfully installed an OTA update perhaps 3 times since owning it.

You are going to have to get very familiar with sideloading the updates. Here is a set of instructions that I created in my "How to Root" thread in the Pixel 3a forum.

If the normal OTA method isn't working - sideload the OTA update

Taking an OTA update should be as easy as the above instructions. However there is another option available to install an OTA update called sideloading. Sometimes the update doesn't appear on the phone in a timely manner and you may want to manually install the update. Other times the OTA update seems to fail for some reason. In the end, you may decide to sideload the OTA instead of trying get it via the update feature on the phone. Surprisingly, it's actually faster to install the update via sideloading than it will be to take the OTA normally. I'll walk through the sideloading steps.....

Optional Step 1 - Uninstall Magisk (so that it restores the stock boot.img). If you find yourself unable to boot into recovery, you will have to restore the stock boot.img. I've run into this issue on some Android 10 images, but not all.

Step 2 - Download to your computer the correct OTA image from here

Step 3 - Connect to your phone via ADB on your computer. You should see the device listed if you type the command "adb devices".

Step 4 - Boot your phone into recovery (type the command "adb reboot recovery").

Step 5 - The phone will have a green android robot with a red sign over it's open access panel. Press the power button and then the volume up button while still holding down the power button.

Step 6 - Select "Apply update from ADB" using the volume buttons to highlight the choice and the power button to select it to enter the sideload mode.

Step 7 - Using your computer, type "adb sideload ota_file.zip" where ota_file.zip is the name of the OTA file you downloaded in step 2.

Step 8 - Once the update finishes, reboot the phone to complete the update process. (See note below about initial boot times).

Step 9 - To obtain root again, please use one of the two root methods listed above

Please note, while the the initial boot doesn't generally take that long there are times when may take quite a while. In extreme cases, I've seen the process take upwards of 20 minutes and longer. I think part of the reason it can take so long is that it optimizes the apps during this boot process. The more apps you have, the longer the process may take. When you take an regular OTA update, the phone will change to a screen where is specifically tells you it is optimizing the apps and counts up as the apps are optimized to give you status updates. When you use the side-load method, it all happens with just the regular boot animation running and without any status updates. Because of this, it is easy to assume something has gone wrong with the boot process while in fact the phone is working through the process normally. If it isn't boot looping (showing the initial power screen before moving back to the boot animation), everything is fine and you just need to be patient and let the phone complete the process.