Subdomain pointing outside webflow - ANY IDEAS?

Hello, I have my client’s website here on Webflow. It turns out that they now want to have a subdomain pointing to a complementary library that is not on Webflow (something like library.domain.com). Their email is on Microsoft 365, and I prefer to keep domain management there as well as the DNS administration because I feel it’s more stable. At first, I tried to move everything to GoDaddy and manage the DNS records from there, but I don’t trust GoDaddy much. I could create the subdomain, but the library’s hosting doesn’t allow creating the record as an TXT as godaddy suggests, the people from the library are asking to create a CNAME pointing to their main site. However, if I do this, it will direct to myclient.com instead of library.myclient.com, as I can’t access folders like a cPanel to assign different paths and avoid interference with the Webflow website, ensuring it doesn’t impact Microsoft services and vital email.

I’ve been considering buying a hosting plan that allows me to have a cPanel, thinking it might give me more control over the domain and DNS. However, I’m unsure if this is a good idea. Do you have any thoughts or suggestions? I hope this doesn’t sound too convoluted.

This is the message I recieved from the library providers:

"Actually, it would be beneficial for us if what you create is a CNAME record because our IPs are not usually fixed (there is a possibility that we may move some of the libraries to another internal server), and in that case, we would have to ask you to change the IP.

Being a CNAME that points to sites.lejister.com, in the event of an IP change, it automatically refreshes for all clients without needing to bother you with any updates."