This meant a new sprinkler was in order, until I realized I could simply replace the internal mechanism of this particular sprinkler. Since Home Depot only carries the complete sprinkler, I figured I would swap out the internals and keep the new housing as a spare. That is, until I realized you need a special tool to remove and install the internal parts, which Home Depot and I did not have, and I didn't want to pay or wait for. So I decided I would just replace the entire sprinkler.
Of course these particular sprinklers can have the water inlet at the bottom or at the side. I assumed this would be a pretty simple job with the inlet on the bottom, since this arrangement would make installation and replacement a much easier task. You could simply screw the sprinkler on and off without even really needing to dig. Any rational person would use the bottom inlet, so of course this one used the side inlet, which would require digging a big hole to allow the whole sprinkler to be rotated and unscrewed from the supply line.
Of course there was a giant root right in the way which made unscrewing the sprinkler difficult (and also may explain why they used the side inlet). I will also note that this project finished my roll of Teflon tape, which I think is pretty impressive. To have enough projects to use an entire roll of said tape is quite a feat, not to mention keeping track of the roll long enough to use the entire ~50 feet.
The new sprinkler went in relatively easily.
After a quick check and confirmation of no leaks, I buttoned everything back up. Not bad for less than an hour of work*.
*And just one Miller High Life