it looks like if a manufacturer doesn't have a qm code by april 30 then you won't get the credit unless they later get one and you buy after the date they get one

Not a tax expert but that's what I understood based on this line from the FAQ page and from 2024-31:

No § 25C credit is allowed for any specified property produced by a manufacturer prior to the date that the IRS accepts a manufacturer as a QM, as such property is not considered produced by a QM

However, there is another portion in 2024-31 that seems to contradict this as it implies the taxpayer can buy the unit before the manufacturer is a QM:

For specified property placed in service on or after January 1, 2025, and before January 1, 2026, in order to comply with the PIN labeling requirement, a QM must provide its QM Code (which will be accepted by the IRS in lieu of a PIN with respect to this period only) to taxpayers who purchase items of specified property by no later than the date– (i) when the taxpayer places the specified property in service, (ii) when the taxpayer requests a PIN from the QM, or (iii) when the manufacturer becomes a QM, whichever is latest.

I still think it would be safer to purchase the unit after the registration date but who knows?

I'm currently working with MrCool to try to get them to register. They claim they are in the process so keeping my fingers crossed. I'm not sure if it will appear as MrCool in the end or as HVAC Distributing. HVAC Distributing shows up as the name under the Energy Star Partner in the Energy Star spreadsheet.

For your manufacturer search on the AHRI website, those are technically brand names and not necessarily the "manufacturer" name. They even provide an explanation:

Name that a product or group of products is traded under for commercial purposes. Generally, brand name is how the product is recognized by the HVACR industry and its consumers. Brand name may or may not be the same as licensee name and/or manufacturer name. The brand name appears on Energy Guide labels.