They will not have a clue.
Dimension wise I don't think you can chamber a 06 in a 303 chamber anyway .
Put the bullet into the barrel end and see what the fit is.
A 303 is actually .310 - .312 bullet diameter. It will swallow the 308 bullet.
I doubt a 303 would even start to chamber in an 06, rim and extractor (and the same for a 303 except the other way, your file matches up as a normal 30-06. Vastly larger o the the rim
It clearly is a 30-06 bolt and 99.999999999% clearly a 30-06 (the tiniest doubt is some really wild stuff needed that is so far fetched as to be impossible but not 100% - this is the real world)
Yours has the US ordinance mark on the front of the barrel and if you remove the rear hand guard you will see that same symbol on the top of the barrel back by the receiver.