If you can use the new certificate with a web browser and not with seafile-gui, then you have to make sure your server also sends all necessary intermediate certificates, e.g.
->openssl s_client -connect $SERVERNAME:443
depth=2 O = Digital Signature Trust Co., CN = DST Root CA X3
depth=1 C = US, O = Let's Encrypt, CN = Let's Encrypt Authority X3
depth=0 CN = $SERVERNAME
0 s:CN = $SERVERNAME
i:C = US, O = Let's Encrypt, CN = Let's Encrypt Authority X3
1 s:C = US, O = Let's Encrypt, CN = Let's Encrypt Authority X3
i:O = Digital Signature Trust Co., CN = DST Root CA X3
In this example “DST Root CA X3” is a trusted root certificate which is known through the certification store of your OS.
My guess is, that your server is not sending the intermediate certificate (1) in this example “Let’s Encrypt Authority X3” issued by “DST Root CA X3”. A web browser usually caches this certificate, so if the browser has seen the intermediate certificate once, it will remember it. The seafile client does not cache the certificate! So if the web server does not send the intermediate certificate the client check will fail.