Looks good.
Big beds, so you will need to walk on them to reach the middle anyway, and yes the compost wants to be firm, not fluffed up or loose.
In dry weather like over most of the UK at present, I would even walk on the beds now, evenly and methodically. This conserves moisture and means that when roots develop, they are not suddenly stranded in mid air.
You cannot compact compost unless its sludgy and poor quality.
To sow, draw a drill as usual, water IN the drill only, unless it’s v damp weather, sow seeds, then draw the surface compost back over.
In dry weather ongoing, walk on the drill after sowing, or tamp firm with a rake.
Job done, do not water until seedlings are growing strongly.
