What kind of sane person is gonna debug and track down a memory leak, though? Just buy more ram

You need to control a domain, so LE can verify you are the controller of the domain, then LE will issue you a certificate saying you are the controller of the domain.

For a wildcard LE cert, you need to use the DNS challenge method.
Essentially the ACME client (or certbot or whatever) will talk to LE and say “I want a DNS challenge for *.example.com”.
LE will reply “ok, your order number 69, and your challenge code is DEADBEEF”.
ACME then interacts with your public nameserver (or you have to do this manually) and add the challenge code as a txt record _acme-challenge.example.com. (I’ve been caught out by the fact LE uses Google DNS for resolution, and Google will only follow 1 level of NS records from the root authorative nameserver).
All the while, LE is checking for that record. When it finds the record, it mints a wildcard certificate.
ACME then periodically checks in with LE asking for order 69. Once LE has minted the cert, it will return it to acme.
And now you have a wildcard cert.

So, how to use it on a local domain?
Use a split horizon DNS method.
Ensure your DHCP is handing out a local DNS for resolving.
Configure that local DNS to then use 8.8.8.8 or whatever as it’s upstream.
Then load in static/override records to the local DNS.
Pihole can do this. OPNSense/pfSense can do this. Unifi can do some of this.

How does this work?
Any device on your network that wants to know the IP of example.example.com will ask it’s configured DNS - the local DNS that you have configured.
The local DNS will check it’s static assignments and go “yeh, example.example.com is 10.10.3.3”.
If you ask you local DNS for google.com, it won’t have a static assignment for it, so it will ask it’s upstream DNS, and return that result.
And it means you aren’t putting private IP spaces on public NS records.

Then you can load in your wildcard cert to 10.10.3.3, and you will have a trusted HTTPS connection.

Here is a list of LE clients that will automate LE certs.
https://letsencrypt.org/docs/client-options/

Have a read through and pick your desired flavour.
Dig into the docs of that flavour, and start playing around.

If it’s all HTTPS, consider using something like Nginx Proxy Manager (https://nginxproxymanager.com/) as a reverse proxy in front of your services and for managing the LE cert.
It’s super easy to use, has a decent GUI, and then it’s only 1 IP to point all DNS records to.

DNS and domains are just human-friendly IP addresses.

You only have 1 public IP address.
So, to access different services you need to use different ports.
Or run a service on a single port in front of the other services that can understand the connections and forward the connections to the actual services - known as a reverse proxy. In the case of http/https, there are plenty of reverse proxies that can direct requests based on all sorts of parameters, subdomains being one of them.

If you are just starting out, I’d recommend a docker compose stack and Nginx Proxy Manager.
Learning containers & docker makes everything easier.
NPM is a very easy to use reverse proxy with a nice GUI, so you don’t have to configure CertBot/ACME or learn the specific config language of Nginx.

If you are unsure of domains and all that, you can try it out for free.
Your computer has a hosts file (/etc/hosts on Linux, I think it’s in system32 on windows). This allows you to tell the computer “for the domain example.com use the IP 10.0.0.200” or whatever you want. You need a hosts file entry for each subdomain.
What this means is that you can run up a docker compose stack on your computer and point a bunch of sub domains to 127.0.0.1, use self-signed certs, and play around with nginx proxy manager and docker.
No money spent, no records published, no traffic leaving your computer.
Zero risk.

There are loads of tutorials out there on NPM and docker compose stacks. Probably some close to your specific requirements.