Would you put the same 12AX7 tubes for both onboard phono and line amp of an integrated?

No, you don’t need to match. Don’t make this harder than it has to be.

Many of us who have been doing tubes for a while, actually prefer to mix different makes of tubes across our available slots. The positive attributes of each tube brand are often additive, rather than working against each other. Like adding different seasonings / spices to a dish. This also makes for infinite combinations to try - but don’t go too far down the rabbit hole. RCAs generally mix great with anything else (Sylvanias too).

You can certainly use the same brand + make all the way through, and sometimes this works great, but especially with Mullards - it could end up being "too much" of that one flavor. I had some amps where if I put in British Mullard EL34 and Mullard 12AX7, it would be like having a quilt blanket over the speakers. Many VACs tend to have an inherent "sweetness" to their voicing, too. I definitely wouldn't overload a VAC with Mullards, and that's certainly not something Kevin ever did (as far as I'm aware).

mulveling, thank you, I think you are right and I will follow your advice.

Again, I currently have Mullard narrow long plates from 1959 in the line preamp, early 50s RCA black plates in the driver slot and Mullard XF2 power tubes. This combination works perfectly with my speakers and for my taste, as far as I can tell. The sound is on the warmer side but not at all excessively warm. Resolution, details, dynamics and bass all good, not to mention soundstage, timbre etc. Early 50s RCA black plates in the phono should complement it very well.

OP: keeping both units periodically maintained, signals tested, is more important than matching similar tubes in all separates! After 100hr  SS devices are stable in terms of performance for next 50000hrs, while tube stuff needs checkup for every 50..500hr depending on how hard tubes are used!