Tangier, Davis' last post about disk subsystems got me thinking. Like you, I found there are almost no references to error -536870181. However -- converting it to hexadecimal = 0xE00002DB. Searching on variations of that hex number leads to the open source file IOReturn.h, which is part of the IOKit framework used in macOS. There we find:
#define kIOReturnNoSpace iokit_common_err(0x2db) // no space for data
IF that is correct, it implies some kind of out-of-space condition during an I/O operation. It's interesting the error happened when *exporting* a file (which obviously takes lots of space). That said, it might not be a normal "out of space" condition.
It could be some transient issue involving memory usage spilling to the page file (which takes more space but is quickly released). It could be APFS local snapshots consuming space, or even a problem with the drive itself.
Re the project repair function, I have a recent copy of your project (minus the media). I tried the repair and it found no problems.
We still haven't time-correlated the above errors from the system log with the "-536870181" error raised by FCP during export. We need to verify those are happening at the same time. Right now it's just a guess.
However I think the kIOReturnNoSpace error is a promising lead. An FCP user on Reddit reported that error -- also when exporting a file. He also reported logged errors referencing VTEncoderXPCService, which is the host process where the encoders run during export. That process itself can take up lots of memory, which can spill to disk in the page file.
Another complication is APFS has a "local snapshots" facility which can also consume space. I think it's supposed to release those when under pressure, but maybe the thread making the I/O call got tired of waiting and interpreted it as a failure.
I suggest you boot the machine in Recovery mode and run Disk Utility First Aid on each disk volume. To run it properly on the Macintosh HD volume, that should be expanded in the left sidebar of Disk Utility, then First Aid should be run from bottom to top, one pass *each* on "Data", "Macintosh HD", etc. Running it in recovery mode gives the best results because all other activity on the drive is stopped.
Disk Utility should update any space usage metadata that might be off. Then boot the machine, check disk space, take action as needed. Make sure there is *plenty* of extra space on all drives.
Once the system is up, I suggest running Disk Utility First Aid on all other drives. Observe the results of each pass, make sure there are no serious errors.
Yes, updated log only if you get the error again. I'd also like any FCP diagnostic reports from /Library/Logs/DiagnosticReports. You can go there in Finder via Go>Go to Folder (enter /Library/Logs/DiagnosticReports), then do CMD+F in Finder and search that folder for "Final Cut". Zip those files and send them to me, but only if you have another error.
If you have another error, please note the date and time (inc'l time zone) and let me know.