It looks like the new Parker 22's and 23's have an option to add a trolling motor with 72" shaft. That option is for the motorguide Xi5 but I think motorguide is no longer branding as "motorguide." Their website says they will be manufacturing as lowrance and simrad brands only now and the prices appear quite a bit higher. I had a motorguide Xi5 60" with pinpoint gps for heading lock, spot locks, etc.. It was good on my 1801. If you can still find one, I'd suggest the 72" for a 23SE, and probably the 36-volt variety, as opposed to the 24-volt. for the stronger thrust.
However, I've been searching for a bit and am leaning toward the Garmin Force Kraken white version in 75" shaft length for a new 22cc. It can flex voltage for either 24 or 36 (both with good thrust), plus I liked the extra 3" in length for staying under while rolling with wakes. Its also a lot more money than the expiring motorguide Xi5's, but is competitve with most other nice models from Minn Kota and Rhodan. Its also less pricey than the powerpole TM. If I end up purchasing before next season, it will likely by the Garmin Kraken.
As for charging, there are a lot of on-board chargers. I had MK 3-bank on my 1801, which can be set for all battery types. I carried on a honda 1100watt generator and ran it in whisper mode to charge the batteries once or twice a season or as needed. My batteries were AGM's. If you want to lighten your load on the boat and from your wallet, go with dakota lithiums. They may end up costing you less by 2032.