Any home warranty experts? A/C part shortage?

[Maria D'Aura]

I have a home warranty on a duplex I recently purchased. The tenant reported the A/C wasn't blowing cold air. I setup a service request with the home warranty and they sent out a local repair company. Repair company said it needs a new compressor. 

The warranty company and not the local repair company orders the part. The warranty company said usually this takes a few days, but currently there is a part shortage so it's taking longer. It's been a few weeks at this point. Last week the company said they don't expect it to take longer than a month, but can't say exactly when they'll have the part.

I know last year there were shortages on appliances and other items. Anyone know if A/C compressors are currently in shortage? This is my first time using a home warranty company and I'm trying to gauge if there is a legitimate shortage and delay with parts or are they intentionally delaying getting the part, could they find it through another source, etc...

Googling tells me this is an expensive fix so I feel stuck waiting on the warranty repair, but the tenant is not happy waiting either.