Hello been designing asnd building for production transformers since 1980s.
1/ Mains 50/60Hz:
0.014" silicon steel laminations are used for low eddy current losses, and high inductance.
Designs can be optimized for a Trise/ambient and to minimize core loss, but tradeoff is cost and avaiablity.
Laminationsfrom Tempel Steel, etc.
Alternative s tapewound toroids or tapewound cut core, but similar or small thickness.
Vendors like Arnold and Magnetic Metals. VERY costly but smailler size and lower losses.
All except toroids are asy to gap is needed.
2/ Audio: To achive a wideband transformer, with good LF response you need a large core area and very thin laminations or tapes.
Bell Labs developed high per materals like Supermendur in 1950s.
The cores are special lams or tapewound trorois or cut cores.
Vendors can be Vaccumsmeltz in Germany or Arnold, Magnetic Metals, etc,
Expect special windings and some small guage wire.
3/ FabL Bobbin and toriod winding machines are automated nowadays but hand machines are also used.
See Micafil /Metor in Switzerland or Adams Maxwell in USA for winding machines.
Bon Chance!
Jon