Yes, that's exactly what I was going for! You can sort by every person's email individually, but this will become difficult if you have many suppliers. You can also use code to find company emails. For example, in my organization we sort the exact way you are, but we go based off of user's names. For us, one table might be:
Filter('My List', LookUp('My List', Title = User().FullName))
If you were going based off of email, you could do something like:
Filter('My List', LookUp('My List', columnName = User().Email))
This code will show a filtered version of the supplier table, if there's a field where you store a supplier's email that's what you'd want to sort by (I called it "columnName" here). You may have to do a little bit of work to the code depending on how you store the data, but let me know.