Can't connect to any SSH server over WIFI (ethernet works fine)

[Moritz von Schweinitz]

Running an up-to-date Debian 10 Buster on a Raspberry Pi 3, I can't connect to any SSH/SFTP server while on wifi. Using a cabled ethernet connection works fine. I can even connect to a server via OpenVPN and wifi, and then connect to SSH using the VPN connection.

I have another (regular) Debian Buster box on the same LAN, and SSH works fine.

The ssh connection always hangs at this very moment, no matter which server I am trying to connect to:

[...]
debug2: service_accept: ssh-userauth
debug1: SSH2_MSG_SERVICE_ACCEPT received
debug1: Authentications that can continue: publickey,password
debug1: Next authentication method: publickey
debug1: Trying private key: /root/.ssh/id_rsa
debug1: Trying private key: /root/.ssh/id_dsa
debug1: Trying private key: /root/.ssh/id_ecdsa
debug1: Trying private key: /root/.ssh/id_ed25519
debug1: Trying private key: /root/.ssh/id_xmss
debug2: we did not send a packet, disable method
debug1: Next authentication method: password
<email address hidden>'s password:
debug2: we sent a password packet, wait for reply
debug1: Authentication succeeded (password).
Authenticated to servername.com ([xx.xxx.xxx.xx]:22).
debug1: channel 0: new [client-session]
debug2: channel 0: send open
debug1: Requesting <email address hidden>
debug1: Entering interactive session.
debug1: pledge: network
debug2: channel_input_open_confirmation: channel 0: callback start
debug2: fd 3 setting TCP_NODELAY
debug2: client_session2_setup: id 0
debug2: channel 0: request pty-req confirm 1
debug2: channel 0: request shell confirm 1
debug2: channel_input_open_confirmation: channel 0: callback done
debug2: channel 0: open confirm rwindow 0 rmax 32768

It then hangs for a minute or two (CTRL+C doesn't work), and then crashes with
packet_write_wait: Connection to xxx.xx.xx.xx port 22: Broken pipe