“Our company currently uses Google Drive through our current company Microsoft email accounts. For example, someone outside our company (client, vendor, partner, etc.) shares folders or Google Docs to our company Microsoft email accounts. How will the migration from Microsoft email to G Suite mail affect this?”
SHORT ANSWER: Yes, there will be an effect but we have a solution for you to use.
ORGANIZATIONAL ACCOUNT vs. PERSONAL ACCOUNT: This issue is similar to the case where you have Google Drive documents through your personal gmail account (except in this case documents are shared to email@example.com account that started out on Microsoft). Essentially, G Suite treats the document sharing to firstname.lastname@example.org Microsoft account as a personal account (the same as it treats document sharing to personal gmail accounts). The conflicting account is a bit of a pain as Google doesn't allow you to easily merge accounts. Basically you had a "personal" account before and now you have a separate "organizational" G Suite account and both accounts use the same username (i.e. email@example.com) so there is a conflict.
CHANGE YOUR “PERSONAL ACCOUNT”: (1) What you need to do is change the document sharing from "personal"firstname.lastname@example.org account username to any account that uses @gmail.com username (email@example.com). (2) Then log into the firstname.lastname@example.org account and share any documents you want to bring over with with your "organizational" account (email@example.com). Once you're done sharing everything and you can access it via your "organizational" account (firstname.lastname@example.org), you can delete or ignore or forget about the email@example.com "personal" account as you won't need it any longer. If you are curious to learn more, click here.