After a lot more digging around, I have a solution that works for now, but I am not really happy with it. Ideally user would only see files inside web root folder and should not be able to go to parent folder. Maybe in the future I will also switch this for a normal FTP server, since they should be easier to configure.
So, the solution is to create user's home folder, "jail lock" user to that folder, create new folder inside user's home folder and mount the web root folder to that new folder. Update permissions and that's it. Oh, and also take care when server restarts, that folders mount again, otherwise user will see empty folder.
Code, for future readers:
# edit SSH config file
$ sudo nano /etc/ssh/sshd_config
# add this to the bottom of file ... the `include` directive does NOT work
Match User [username]
# force user to use SFTP only and change their directory to desired one
ForceCommand internal-sftp -d /[folder name]
# allow password auth for this user only
PasswordAuthentication yes
# user's root folder (must have root:root privileges, otherwise user can't log in)
ChrootDirectory /home/[username]
PermitTunnel no
AllowAgentForwarding no
AllowTcpForwarding no
X11Forwarding no
# restart SSH service, so that it picks up updated config file
$ sudo systemctl restart sshd
# create new user
$ sudo useradd -d /home/[username] -s /sbin/nologin -g [isolation group] -m [username]
# create password for that user
$ sudo passwd [username]
# give write permissions to the group (should be there already but didn't work, needed to do this)
$ sudo chmod g+w /home/[isolation group]/[website root]
# create a folder which will be shown in user's FTP client
$ sudo mkdir /home/[username]/[folder name]
# user's root folder (must have root:root privileges, otherwise user can't log in)
$ sudo chown root:root /home/[username]
# mount web root to created folder
$ sudo mount -o bind /home/[isolation group]/[web root] /home/[username]/[folder name]
# re-mount folders when server restarts
$ sudo nano /etc/fstab
/home/[isolation group]/[website root] /home/[username]/[folder name] none bind 0 0