My bet is the added circuit wouldn't create an actual overload.
The first 4 requirements are kind of redundantly covered by the requirement for a NEMA 14-30 outlet, that is a 240v 4 wire 30A outlet, which is the proper size for 125% protection for 5500w/23A.
The Code method for determining calculated service capacity is a little involved adding watts per square foot, code required and actual additional dedicated circuits, determining motor/fan sizes and demand factors. There are samples online.
This load calc is required at every new installation. Whether this calc would result with bad news could only be guess with info provided. It seems in my experience inspectors used to rarely require a new calc for a new single circuit, kind of like they presumed it was covered in the sq. ft. calculation. But it seems like nearly every new 14-30 now is a evse outlet, which certainly doesn't fit the sq. ft. narrative and many jurisdictions are requiring new load calcs with every 14-30 or larger circuit.
240v circuits require a wire from each of two adjacent 1" spaces. It has been suggested to use a BQC quad breaker that doubles up taking two wires from each of those spaces to feed two circuits. These can only be used in spaces designed and Listed to accept these special breakers. Breakers that are allowed will be listed on the panel cover label. It is likely new enough to be designed to accept these breakers due to the type of labels shipped with the panel, but that isn't proof. The Square D breaker also won't be shown on the label as approved for this panel. If there was no GFCI recommendation or requirement then (assuming the AC breaker is 30A) buying one BQC230230 breaker, installing it in the space the alien Square D breaker is to serve both the AC and brewing equipment and you would be done. This method seems simple because it changes out one breaker that has to be changed anyway.
Next equipment recommendation/code requirement. The GFCI recommendation is likely there to encourage you to check NEC requirements for the location you are installing the equipment. New in the 2020 NEC (which your jurisdiction may not have adopted yet) is a requirement for 240v circuits be GFCI protected in all the locations that 120v circuits previously required protection (like basements, sheds, and garages).
This brings us back to the quad recommendation. GFCI protection to my knowledge is only available for 240v circuits at the breaker, which requires two full dedicated beaker spaces and we just put it on a shared space, making the previously recommended replacement of the alien breaker with a quad not quite that easy. But that is easily resolved, put the new GFCI breaker in the dryer location, land the brewing equipment there, and move the dryer wires to the location on the left where you installed the BQC breaker.