As to kernel driver support, apparently the linux 6.8 kernel (as in Ubuntu 24.04) will work with this hat, but with varying success, depending on what M.2 wifi module you add (Intel BE200, AX210, and AX200 modules are reported to work).
All Intel wireless cards are unusable for AP functionality (only very limited on 2.4-GHz-only), likewise those aren't DBDC either - so you'd have to decide between either 2.4 GHz operations XOR 5 GHz (but you can't operate an AP interface on 5 GHz either way, so… crickets).
If you were looking at 'real' AP mode- and DBDC capable M.2 cards, you're immediately hit with the current draw (3A on 3.3V!) and quite massive heat dissipation issues (considerable heatsink hard-required, fan probably as well, these cards can cook themselves to death), which are unlikely to be met by the RPi5 and this hat. You can use the forum search for prior discussions of this topic, predominantly with x86_64 hardware in mind, it just isn't likely to work at all/ well enough.
Like for x86_64, the only sensible answer is a dedicated plastic AP (mt7921a+mt7915DBDC, filogic 820/ 830, ipq807x, …) running OpenWrt, it's going to be considerably cheaper, faster and more reliable.
I have an AX210 card which I connected via an M.2 M-Key to M.2 ngff (AE-key) and M.2 M-key to PCIe adapter to the RPi 5 board.
In the 2.4 Ghz band it works ok so far and it perfectly fits my purposes since I plan to connect my phone via USB to the router and then just have an 802.11 mesh node activated on the card. If I need an additional AP I can use the onboard wifi module. But again, my project is to built a manheld radio similar to the MPU5 which is always carried on my person.
If you're planning to built a router especially for AP purposes then this card is not recommended...
Then your solution is kind of too expensive, a small USB MT7610U dongle (802.11ac 1x1 with 5GHz band support) is dirt cheap with decent throughput. The onboard WiFi as AP....er....you can probably forget about it since it's Broadcom.