Does Apple still support Time Capsule?

This depends on what you mean by "support".

The Time Capsule and other AirPort routers were discontinued in April 2018 and the warranty on the product was one year, so there are really no Time Capsules still covered by the regular warranty unless a user has AppleCare in effect on one of their Macs, in which case the Time Capsule would be covered for up to 3 years from the purchase date.

Apple did issue a firmware update for the Time Capsule and other AirPorts about a year and a half ago, but there have no other updates since that time. At this point, security updates are long overdue, but Apple remains silent on their plans.

My opinion would be that we saw the last update about a year and a half ago.

If you are willing to pay Apple $85, or whatever the current rate for phone support would be, that might be an option if you have an issue that needs to be resolved.

Apple does not and has not ever offered any support for parts or repairs for the Time Capsule since they consider it to be a sealed unit, but an independent shop might be do some repairs if they are required.

If Apple issues a firmware update, the indicator light on the front of your Time Capsule will blink amber to let you know.

Open AirPort Utility and click on the picture of the Time Capsule

Click on the Update button