2017 MacBook Pro less than 200 battery cycles, but battery needs service

Here is a link to all of the Service Bulletins for Apple Devices --> Apple Service Programs - Apple Support

If your device is not covered under a service program, you'll need to schedule an appointment at your Apple Store Genius Bar and they can explain the battery replacement costs.

Battery Cycles is not an indicator of battery health except when the Battery Cycle gets near 1,000 cycles which indicates the likely end of life for the battery, otherwise just ignore the Battery Cycles. Apple may also use the Battery Cycle Count to determine if a battery qualifies for warranty coverage.

Batteries run on a chemical reactions and with Lithium-ion batteries this is a very delicate balance where a lot of things affect battery health. The battery temperature plays a role (even when storing the laptops) as does every bump of the laptop which could possibly affect the delicate internal connections within the battery cells. Having a Lithium-ion battery completely discharged for any length of time can weaken and even damage a Lithium-ion battery. Then of course there can always be random glitches in manufacturing or materials (even a bit of dust during manufacturing can begin to introduce a potential premature failure).

"Service Battery" usually indicates a hardware issue has been detected, but this condition has been replaced by a more generic "Service Recommended" beginning with an update patch to macOS 10.15 Catalina which also indicates a "consumed" battery which has a capacity of less than 80% of the original Design Capacity.

I don't believe there is. The only service programs I've heard of for Mac batteries have to do with safety issues and not longevity per se. My Mac's battery came out of the box with about 94% normal new battery health back in 2015. It wasn't eligible for any warranty or special service on that basis. It finally gave the service battery warning after about 6+ years and was also slightly swollen (pressing out against the trackpad). It had less than 200 cycles when the nominal rating was for 1000 cycles. But I was able to pay for a battery replacement at an Apple Store.

There was a time when Apple had service replacements at a lower price than retail replacement batteries, but that was only for batteries that the user could self-service. I had a swollen battery with less than 200 cycles (300 was the nominal rating) and could get a service replacement. I still had to pay for it, but it did cost less than a retail replacement battery.

But for the batteries that Apple doesn't consider user serviceable, there is nothing. It either is eligible for warranty service if it happens within the warranty or it's not after the warranty is up.

There is always a possibility, but normally it is not necessary if only the battery needs replaced. Apple assumes the user has backups.

You should always have frequent and regular backups of your computer and all external media (including the cloud) which contains important & unique data. FYI, it is impossible to recover accidentally deleted data from an SSD after the Trash has been emptied, plus an SSD can fail at any time without any warning signs. Also, the SSD is integrated onto the Logic Board with most new Macs including yours, so if the Logic Board has a failure, then it may be impossible to access the data on the SSD.

Make sure you fully backup your computer before you go.