Capacitors bulging/leaking (especially in power supplies) is common enough, but normally the issue “ends there” i.e. normally there is no damage done to the main board nor to the rest of the PSU circuit.
Personally I would:
order the replacement PSU and mount it.
change the capacitors on the old one, test it works and then keep it as spare.
Specifically the CCR-1036 PSU’s (it may depend also on model/revision) are known troublemakers, JFYI:
We’ve had several of those PSUs fail in 1036s. We usually just replace them. At least so far we haven’t had a replacement fail, but they might need another year or two of service to equal the lifespan of the originals. If those fail as well we might not have any choice but to repair them. I’m not sure we can get the replacements anymore. I suspect it would be possible to hunt down a suitable 3rd party replacement as well, but hopefully we won’t have to.
After all it is a “plain” 24V 4A PSU, not rocket science, you can also use external power bricks, they are common because quite a few monitors/TV’s use them, besides low voltage passive PoE, but really, replacing the capacitors is easy, cheap and works in most cases.
The original one should be 17x7x4.5 cm, so rather bulky, I think most reaidly available no-name ones are smaller than that.