Genius bar won't do battery service for my iPad 7th.

That’s kind of the way it works. It has to be in good working and cosmetic condition, which involves a once over and a standard diagnostic to make sure it works. It’s worth it to Apple as parts for refurbishing, and if it’s not in good shape and good working condition, they will only offer an “other damage” replacement. If it doesn’t turn on, they have no idea if it works well. A battery service is just a replacement at a lower price point with an exchange of a known, working iPad (again, useful for parts). But it’s all simplified into two price points.

I wouldn’t necessarily recommend it for everyone, but one alternative is 3rd party battery replacement. I’ve had it done before with varying results. Part of it was that the screen was cracked, a friend had it done overseas cheap, and they threw in a battery (didn’t cost much more) since it was already cracked open. The battery didn’t work great though. It didn’t seem to keep a charge and eventually failed. But it did work for a while.

I have seen the 64GB 9th gen iPad on sale right now although I’m not sure how long. $269.99 plus tax at Amazon, Best Buy, and Target. That might be a decent replacement considering that it’s newer and more powerful, along with being the last iPad that will use Lightning.

OK - I thought the 9th gen iPad was a good bargain when I got it for $312. But I guess it's gone down in price with the 10th gen out but the 9th gen still available.

For better or worse, Apple has chosen a "repair" model where everything is reduced to replacement with a service unit (may be new or refurbished). I suspect when they receive anything in exchange, they'll never reuse the display or the case. But even if the case or display are trashed but the internals still good, they charge the same for replacement as for a completely dead iPad. This is all baked into the replacement price, where Apple has to produce enough parts that may be combined with previously used parts to make working replacement devices.

But Apple generally doesn't replace batteries. There are some hints that maybe newer models can have Apple replace the batteries in the same device to be returned to the user, so in that case they might be able to inspect and do a check to see if maybe a good battery (just for testing) works in order to do the diagnostic and perhaps then replace the battery with a new one if everything else is fine. But in your case it sounds like they aren't really equipped to do that.

No.