You are confusing things. The models in the boardgame all have the backpack but OW mentions that normally the gun comes with a hip mounted 10k battery and the 25kg backpack is a separate item.

And the issue is not "can the charge packs be recharged?" as that is obviously possible but it takes time. Minutes of time that is not helpful during combat when seconds matter.

And for OP: Yes, you can carry several of the hip mounted packs and change from one to another during combat. Preferably you carry more than one of the 30 shot packs into combat and conserve ammo because the Hotshot packs are annoyingly heavy and easily run out of ammo/charge.

You can even have several of the backpacks (hopefully keeping the spare in a vehicle or something) and change them during a mission as well as long as you have the second pack somewhere that you can reach. Heck, if it's in the vehicle and there's a pause in battle you can put the other pack into recharge while using the full one.

My impression in general is that the Hotshot lasguns are meant for brief but important battles rather than prolonged sieges and such. The low ammo is not so much of an issue when you do one brief fight and then either fall back (having destroyed or sabotaged something important) or the reinforcements arrive to secure the location you just conquered.

Also as a pro-tip. FFG keeps changing the stats on the backpack ammo pack and one of the rulesets simply said "5 x the capacity of a regular magazine" and that's what my group always goes with, more than enough shots for the Hotshots in that to last a mission.