My opinion for what its worth...
I would aim for something that can run Dirac DLBC, and will hopefully get DL-ART late this year or early next year.
The bass management of DLBC is what you are aiming for, and the ability to get full spatial roomEQ once DL-ART becomes available.
You other requirement is based on your speakers - you need something with enough power to make a relatively difficult (low impedance) speaker "sing" - so it needs to have a robust power supply capable of providing enough current (rather than power) for your speakers.
Typically 120W@8ohm will be ample for most rooms and most setups - but most amps (and AVR's) provide no information on what it can put out into 3 ohm... if you are lucky the amp you are considering will have been independently tested at 2 ohm... and that may provide a reference point.
In terms of AVR's - my target would be something capable of 7.2.4 in terms of processing, and in terms of power, you need a beefy power supply and more than 120W@8ohm, OR you need an external amp suitable for your speakers, and in that case, the AVR would ideally be able to handle the remaining (surround & height) speakers - which are typically a much more benign load, and require much lower power/current in any case.
If you are planning on sticking to a 5.1.2 setup (ie: no multiple subs) - then you may be able to step slightly down and save some $ in the AVR, however even with a single sub, DLBC can take advantage of the full range capabilities of your main L/R speakers... so there are gains to be had from DLBC - and DL-ART come 2024 will be able to take this a notch further.
If you accept going for only Dirac or Audyssey (without aiming for DLBC) - you could go for the Integra 3.4 (7.1.4 pre outs) with an external amp for your mains - this is potentially the most economical AVR with Dirac and full pre-outs - the Onkyo NR7100 or Pioneer LX305 provide alternatives, but only provide pre-out for the mains... so more limited in terms of future proofing.
The next series up in that family (Onkyo RZ50, Pioneer LX505, Integra 5.4) have a little more power, and can process an additional pair of channels, they have full pre-outs.
These are all Dirac Live full range AVR's... and the upper models may be enough for your 702's... maybe... (a case of "suck it and see")
The Integra 8.4 has only just been announced, (and many of us are expecting at least an Onkyo equivalent and perhaps a Pioneer equivalent to be announced shortly...) - this is a 7.2.4 AVR, but with substantial amplifier upgrades - it has internal amps for all 11 channels, and is rated at 150W@8ohm stereo - with what looks like a robust power supply.... this means it should be able to handle your 702's quite easily!
It also is launching with Dirac DLBC as an option, and most likely will have DL-ART available in late 2023/early 2024 (at a guess).
Other options are the D&M AVR's - the X3800 has all the required processing, and should have Dirac available shortly (but Audyssey is no slouch either) - DLBC should be available next year, and potentially DL-ART - the amps are the weak point, I would look for an external amp for your mains if going in at this level.
If you go up a notch to the X4800 (and marantz equivalent) - then I would be tempted to "suck it and see" - same as for the Onkyo RZ50 level - it may have enough power for the 702's or it may not.
Another option might be taking a step back a generation and going for a Denon X6700 or Marantz equivalent, and sticking with Audyssey - there could be some bargains out there at that level.... it is the previous generation, no Dirac option there, but an excellent AVR, with enough power to probably handle the 702's well - and all the current codecs, etc...
Personally my setup is still 5.1 - and I am preparing to move it to 5.2.4... I am hoping for an AVR which will support DL-ART, which I think will provide a paradigm shift in terms of performance... I find the Integra 8.4 to be the most exciting recent product, and almost a bulls-eye for my target needs... I too have demanding speakers, with impedance bottoming out at 1.6ohm - so a "beefy" AVR, where I can simplify the setup and remove the amps I am using for the mains at the moment, is attractive... and the AV10/AV1 models from D&M are too rich for my budget.
Hope that helps