OP,
I do not own a 338 LM but i have shot a sako like the one pictured a number of years ago. I have no idea the ammo but I remember being astonished by the grain weight. I shot maybe 15 rounds or so.
I found the recoil pretty manageable with the brake that was on it when shooting prone. Loud as EFF tho. With ancient dust sifting down from the range roof with every shot.
I no longer shoot prone due to injury (i also no longer shoot thumpers) but even with my lesser short and AR actions, there is more “felt” recoil on the bench than prone.
Check out some MDT vids on natural firing position and how to position your bod relative to recoil path. It helps.
Or leave the 338LM to young men in uniform. Lol.
bipods are not part of mitigating recoil in my experience although they do add mass which does help marginally.
If u are shooting 338 LM however, a bipod wud be standard I wud think. What else??