Dennis, in my opinion the article I posted covers the branch circuit wiring to the Tub. If a feeder is installed it would have to comply with 680.25 which would rule out NM or SE cable as wiring methods.
If you feed the tub from a main panel and install a disconnect that contains a gfci then the wiring from the main panel to the disconnect is a feeder. The art. you stated says I can use any of the wiring methods of Chapter 3 inside the dwelling so se cable would be allowed IMO. The copper ground would be needed from the disconnect to the tub.
No 680.25 requires a wiring method with a insulated equipment ground a covered equipment ground is not an option for a new feeder to a pool panel. your feeder will have to be in conduitCan you run a ser alum to disconnect then go copper to the tub connections this is an outside hot tub.
Also how is the ampacity of SER alum determined 60 or 75 c.
(A) Wiring Methods. Feeders shall be installed in rigid metal conduit, intermediate metal conduit, liquidtight flexible nonmetallic conduit, rigid polyvinyl chloride conduit, or reinforced thermosetting resin conduit. Electrical metallic tubing shall be permitted where installed on or within a building, and electrical nonmetallic tubing shall be permitted where installed within a building. Aluminum conduits shall not be permitted in the pool area where subject to corrosion.