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I'm looking to cut 3 pass-through mortises (2"x6" long) on each of eight
large pressure-treated square timbers (8"×8" wide x 8 feet long) for a small
post & rail fencing project.
I've cut mortises on smaller thickness using just hand tools (drill, chise,
wood file). I can't justify buying a plunger router or drill press just for
this project and hardware companies near me don't rent them out. My plan is
to purchase a longer drill bit, drill numerous holes along the inside
edges, chisel out an opening on each side, use a sawsall tool to cut around
the perimeter, and use an oscillating tool to clean up the edges. This will
take some time since I have 24 mortises to cut. Not needing a tight fit
since the rails will be loosely placed inside the mortises. Any other
suggestions on how to do this easily with hand power tools?

Old school would be to use a mortising axe... For example
https://www.youtube.com/watch?v=yoT7KaeWmHY

It would be quick in PT... The beam in the video is dry hardwood...

If you find an old one you could sell it when done and it may cost you
nothing for this project.