How to make a 10 year old electric bike battery work better?

As said, the batteries need replacing. They have a limited lifetime, regardless of use. You don't say if they are lead acid or lithium - if lead acid, they will certainly stuffed.

If Lithium they could last many more than 10 years, but only if stored correctly. If replacement batteries cannot be purchased the best option is probably a rebuild. Virtually all battery packs are made up a collection of standard size cells, a rebuild involves stripping the battery and rebuilding with new cells. Cell quality and price varies a lot, so shopping around for the cheapest is not always the way to go, but paying more does not mean you are paying for better quality cells. When selecting a rebuilder, ensure they specify the cells they will be using - ideally a branded named once such as Panasonic or Sony, sourced from a reputable supplier. There are a lot of counterfeit and low quality cells being sold these days.

Changing the connectors to use a different model battery pack is also an option, but you would need to know what you are doing. By the time you source a new battery and installed matching connectors you are likely close the cost of a rebuild.

There are two parts to this question

1. A 10 year old bike that has been out of use for a while

Check tyres for cracking and flaking. Inflate, and if the tubes don't hold air then replace them (patching tends to be ineffective when the whole tube is old.)

Brake pads also go hard with age - if the brakes are poor then replace them.

Rust - chains and cables could rust-up given the storage. Its often possible to rejuvenate a chain, but a cable that doesn't move well normally needs replacement on inner and possibly outer.

2. A battery that hasn't been used for 10 years.

Well if the battery can't supply the power needs, then it has lost capacity over time. That it still works at all is amazing - I suspect the battery was charged a couple of times in the decade of storage.

You have four options - replace the whole pack, repack with new cells internally, or hack some other form factor onto your bike. 24V is achievable using two 12V sealed lead-acid batteries, although you'll need a different charger. The bike won't care, though the "power remaining" gauge could be off.

Outside Box thinking Remember you can always leave the dead battery at home and have a rideable bike. It will be heavier due to the motor and wiring, but without a battery at all will be lighter.