I don’t think there’s anything technically wrong with “the previous person who held this position”, but it does sound overly formal and stilted. I would re-cast the phrase. There’s nothing wrong with using “last” here, even in very formal writing.
“previous person” gets 119,000 Google hits, and the first page of hits appear to be from native-speaking English sources.
As to “budding sophomore”, this is wrong in my opinion. The word “budding” implies being at the preparational, aspiring or beginning stages of a long-term career/profession/hobby/activity.
When one is a sophomore, one simply is a sophomore (a status lasting one academic year, a very short time). It’s not some long-term goal being worked toward.
On the other hand, “budding journalist” or “budding scientist” is OK.