you can usually spot linear power supplies because they’re big and they get hot - there’s a big transformer in there and those are (relatively) expensive. these use coils to drop voltage.

the smaller, cheaper and more common switching power supplies chop incoming voltage up at high frequency (which is then filtered), which dumps radio frequency garbage all over your household power rails. but they’re super common and very efficient.

almost all gear can cope with noisy power though. there are voltage regulators in all your equipment to smooth out spikes and they normally work great.

in practical terms, upgrading a power supply might see a change in mains frequency hum (+ harmonics), or noise floor. unlikely to lead to dramatic audio performance changes… maaaybe better transient handling but if your equipment is that close to operating limits the power supply is probably not going to fix it. a bad linear power supply will be worse than a good switching power supply though. i wouldn’t bother doing this without measuring audio performance because otherwise there’s no way to figure out if it’s getting better or worse.