No disadvantage to the Tesla vehicle or battery when charging using Level 2 (240V) at the maximum supported 48 amp rate of the Tesla Model Y versus lower amperage. (Some data exists that charging at 40 amps might be slightly more efficient.) 48 amp charging may require the Tesla vehicle to perform some additional cooling of the charging components, possibly the battery. The Tesla Model Y will automatically cool (or warm) these components as required.
The industry standard Level 1 (120V) / Level 2 (240V) in the US and Canada is the J1772 connector. Tesla vehicles sold in the US and Canada use Tesla's connector. To charge a Tesla vehicle using a J1772 charging connector you simply use the provided Tesla SAE J1772 charging adapter. This adapter is included with every new Tesla vehicle sold in the US, Canada. Additional Tesla J1772 adapters are available from Tesla's online store at Tesla.com for ($50 US). In this way you can keep a spare adapter or have one at home and one in the vehicle at all times.