All true. Only to add that whether the little 8 is there or not makes no difference, the historical convention has been to miss it out, some modern editions include it but at a guess probably the minority. Some other transposing-by-octave instruments take the same approach, from memory, the double-bass (down) and the piccolo (up) leave the 8 out.
Simon Ambridge Series 40 (2005)
Trevor Semple Series 88 (1992)
Louis Panormo (1838)
Alexander Batov Baroque Guitar (2013)
Simon Ambridge 'Hauser' (2018)