If I want to open a file from Lightroom to edit in Affinity and appear back in Lightroom, I just open the file via Lightroom Edit In -> Edit in Affinity -> Edit a Copy. I have Lightroom set up so that my external editor is Affinity, and it saves as PSDs. I do whatever edits I need done in Affinity, then Export as PSD, overwriting the one Lightroom had just created. When I'm back in Lightroom, the edit is there, with no need to synchronize the folder.
I generally save as PSD just so that I can still have access to the adjustments I made on each layer later on. It also saves to the same file format as Lightroom, while with tiff, Lightroom saves as .tif and Affinity as .tiff so it doesn't overwrite the file that Lightroom creates. To automatically appear in Lightroom without synchronizing, it has to overwrite the file that Lightroom created.