Mirror lock-up only removes vibration from the mirror. At 300mm, blur can still come from shutter shock, tripod/head flex, an extended center column, wind/touching the camera, and simple subject-to-camera vibration during a slow exposure.

Your 1/25 s vs 1/60 s comparison strongly suggests motion blur/vibration is a big factor. A sturdier support helps: keep the tripod low, avoid extending the center column, add weight, or test with the camera resting on a soft support on a solid table to rule tripod vibration in or out.

The first focus series also suggests autofocus accuracy limitations. Viewfinder phase-detect AF and the lens focus motor may not land exactly at the best focus point every time, while Live View can appear sharper because you’re judging focus directly from the imaging sensor view.

Also, the lens itself may simply be soft at 300mm, with some chromatic aberration, so not all softness is vibration.

Practical fixes: use a faster shutter speed when possible, improve support stability, increase the delay if testing, and use careful Live View/manual focus for critical shots.