Thank you very much for pointing me to the right direction !!!
I’ve found the solution with the link you’ve provided : Could not load album - Plugin, SSL handshake, Network request error - #9 by pixel24.
For me, the workaround was to reinstall openssl1.1.1 (following this post : https://askubuntu.com/questions/1403837/how-do-i-use-openssl-1-1-1-in-ubuntu-22-04).
# download binary openssl packages from Impish builds
wget http://security.ubuntu.com/ubuntu/pool/main/o/openssl/openssl_1.1.1f-1ubuntu2.16_amd64.deb
wget http://security.ubuntu.com/ubuntu/pool/main/o/openssl/libssl-dev_1.1.1f-1ubuntu2.16_amd64.deb
wget http://security.ubuntu.com/ubuntu/pool/main/o/openssl/libssl1.1_1.1.1f-1ubuntu2.16_amd64.deb
# install downloaded binary packages
sudo dpkg -i libssl1.1_1.1.1f-1ubuntu2.16_amd64.deb
sudo dpkg -i libssl-dev_1.1.1f-1ubuntu2.16_amd64.deb
sudo dpkg -i openssl_1.1.1f-1ubuntu2.16_amd64.deb
After this install, everything is fine with Picard !!!