Which 4* engine are we thinking for Anby, Anton's signature, the event one with crit %, or the BP one?
All 5 relevant ones seem good.
Anton's give her a 50% increase on all her attacks after using energy, with only 5 seconds of downtime, because she only does electric damage, no physical, this sounds like it can offset the lower crit damage
Starlight engine would pretty much give her a permanent 37% (~45%) increase to attack, which honestly sounds like it might out dps anton's
Guilded blossom reaches ~35% and additional increase to EX, this might be the weakest option.
Desire gives her 20% crit rate, anby gets a natural +10 on her team up, so that's 35% crit without making any effort; it also has a nice 20% increase to attack, but this is situational and might be harder to keep up.
BP rotor is the same as desire, but it has a more consistent extra 7.5% attack that's up at all times, so I believe rotor slightly edges out desire in longer encounters.
The reason why blossom seems like the weakest, is because anby actually has pretty low multipliers, so the increase to EX attack isn't really that impactful, and certainly loses to starlight engine if you have that one maxed out.
Anby also actually wants as much crit damage you can give her, since her passive scales off it, but of course to proc it you'd also need some crit rate; anywhere between 30-40% crit rate should work great if you can get her crit damage above 100%, this means that canon rotor is probably the best option, since you get the crit rate required plus a little bit of extra attack on top without any effort, and then you can just pile on crit damage stats on her discs (and hope you get some attack as well).
If you have harumasa's w-engine and you plan on replacing him with anby, just use his, it's pretty much her second best option.