New mini split ac on existing Spa disconnect
You either need to run a ground or get rid of the outlet

Right now, the GFCI hooked to the disconnect in your picture effectively bootlegs ground off of neutral, and the disconnect box itself is grounded via its neutral as well.  This means you either need to run a ground wire (10AWG copper will do) from this disconnect back to the main panel or the grounding electrode conductor system (by any path you can manage), or re-run the feed to this disconnect with a new cable (12/3 W/G will do since this is now a 20A circuit through and through, even).

Of course, you can also remove the GFCI and its feed, and then simply nut off the white in your cable to the mini-split as unused, landing the bare wire on the existing ground lug.  This technically abuses a white wire as a ground, but given that it's not also performing the function of a neutral at that point and that it runs directly back to the main panel, it's not going to be a major issue, practically speaking.  Of course, if you're going through this work, you could just remove this disconnect altogether given that it seems to be in a rather odd/useless place, replacing it with a simple junction box and a new run of 12/3 from the j-box to the main panel.