Text-based conversations between users with searchable history in Microsoft Teams Free
It is no longer possible to export Skype chats. This feature was replaced with export of logs of calls made to phone numbers when using the Skype Dial Pad site. Additionally, these logs cover only calls made within the last 30 days.
The only chat export option available now is the Teams export page.
https://teams.live.com/dataexport
However, if you have not actively used Teams prior to December last year, the Skype chats will not be available in Teams and cannot be exported.
https://support.microsoft.com/en-us/skype/skype-is-retiring-in-may-2025-what-you-need-to-know
You should also be aware that Skype chat history older than April 2017 was not have been saved in Cloud.