I think technically, in terms of "removals" based on an immigration judge ordering it, Obama still has the record. For "repatriations" which includes "removals", "returns" (no order, can be voluntary), and Covid-19 health related "expulsions", Biden holds the record.

I think data availability has been poor during the Trump administration, but from public numbers that I could find for spring of this year, it's not clear that even with all the raids the Trump administration is actually deporting more people than prior administrations ... but perhaps the goal is to keep more people in detention.

https://ohss.dhs.gov/topics/immigration/immigration-enforcem... https://ohss.dhs.gov/topics/immigration/yearbook/2019/table3... https://usafacts.org/answers/how-many-people-were-deported-f...