You click on your Outlook contact start chat and it open up the new MS Team instead of Skype?

Once you have installed the New MS Team, the software would overwrite the registry to change the default instant messenger application.
Important
Below steps are based on Windows 11 22h2 (OS Build 22621.3737) and M365 Outlook 2405 (Build 17628.20188).
Before you start with below instruction, do visit below post to retrieve your SID first.
* How to get current user Security identifiers (SID)
Follow below steps to change back to Skype.
Step 1: From your keyboard, Press and hold on “Windows” + “R” key.

Step 2: Enter “regedit” in the Textbox as shown below and click on “OK“.

Step 3: Below “Registry Editor” window will be presented.

Step 4: Click on “>” beside “HKEY_USERS” to expand.

Step 5: Click on “>” beside your own SID, for example for my case is “S-1-5-21-1216582894-834684500-1334827815-1460374”.

You may visit How to get current user Security identifiers (SID) to get your SID.

Step 6: Click on “>” beside “Software” and proceed with next step.

Step 7: Click on “>” beside “IM Providers” and proceed with next step.

Step 8: Double-Click on the “DefaultIMApp”.

Step 9: Change the “Value data” from “MsTeams” to “Lync“.

Step 10: Click on “OK” once the “Value data” is reflected as “Lync“.

Step 11: Exit your “Outlook” application if it is open, relaunch the application for it to take effect.