For future reference, I managed to solve this by creating a trigger in the database table itself. The issue seems to be that because the record already exists, AppSheet won’t use the default value formula to calculate an empty column, since that column has already been “set” as empty/null by the original database. Like I said in a previous comment, if the record was being created in AppSheet as a brand new row, then I could use a default value formula to calculate the template/background image without issue (eg. using the LOOKUP function I referenced).
Since I already knew the template image’s values (a text filepath in “template table”), I simply rewrote the LOOKUP AppSheet function as a trigger in the MariaDB table that runs before insertion, reads and compares the record’s Chassis column in an IF-ELSEIF statement, then sets the ConditionDrawing1/2 values of that row to the appropriate text filepaths that match the relevant template images. Then, when a user edits the drawing in a form, AppSheet will automatically save it as a new image and change the column value appropriately (which saves the template image from being overwritten, which was my biggest concern).
There’s probably a prettier/more efficient way to do this, but for now this appears to be working for my needs.