Could I apply for the Tier 2 one day before my Tier 4 expires?

I am currently on a fixed-term contract at an organization I really love. They recently offered me a position but unfortunately the grade level was too low and they felt it did not fit in an eligible SOC code. However, another position has opened up at the organization and it is a way higher salary and grade and could fit into an eligible SOC code. However, the interviews aren’t until the 17th of January and my Tier 4 visa expires on January 23rd.

Hypothetically speaking, if I was offered the position on the 20th of January and the company could produce an COS that same day, could I technically apply for the Tier 2 visa on the 21st even 22nd of January?

Is it necessary to have the biometric appointment prior to the expiry date of your current visa? Or once I hit “submit” on the tier 2 visa application does that qualify as waiting for a decision? I was told in a consultation with an immigration lawyer that as long as you apply for the Tier 2 visa before your expiration date, even if it’s just a day before, you’re not at risk of being considered as overstaying? However, does that include before the biometric appointment?

Thank you!