You issue with learning a ERP from scratch for a hospita ls going to be that a ERP is basically a canned system. That mean that when installed it has a lot of base functions/features/modules it can provide a organization, but ultimately how they are set up and actually utilized is often up to the organization and things can be "simple" or very complex depending on the other systems that the ERP is interfaced with.
If I were you, what I would do is look into and do a little research on healthcare ERP systems and find the common modules or pieces you want to learn first. Oracle, Microsoft Dynamics, and Lawson are the most popular in hospitals so look at how those are used withing healthcare ERP. Those are also very expensive, so go get a popular free ERP with great support like Dolibarr ERP and install it and begin training yourself.
Dolibarr ERP is prob one of the most popular open source ERP's in the world so there is a good amount of help and documentation out there on it.
Here is some others that are popular https://opensource.com/tools/enterprise-resource-planning
I used InvoicePlane in the past and it was awesome in terms of setup-interface-usage-customising.
Dolibarr might be useful for you to have projects with linked timesheets and invoices all in one interface. You can e-mail the invoices from within the system too. You can also create proposals/orders/invoices (on screen and pdf) and also log payments.
Dolibarr continues to grow and has a strong user and developer database. See this Retrospective of 2021: https://www.dolibarr.org/2021-retrospective-dolibarr.php
If you know PHP, you should be able to customize Dolibarr. Not that inventory for the MRP feature is available from v14 only.
I think that industry may well err on the side of Customer Relationship Management (CRM) suites. There do seem to be some open source ones which can sit atop PostgreSQL, such as Dolibarr (Never used or needed, just know these things exist via web searches for 'open source crm postgresql').
You could also perhaps go a half step and connect LibreOffice to your database in a Microsoft Access as forms gui to a central database sort of role, and build basic CRUD forms in there.
I started playing around with Grocy. It's more geared towards the kitchen/pantry, but could really be used for anything.
I also tested out Dolibarr, which is definitely overkill (I was testing it out to see if it would be suitable for a friend's small business), but I'm really thinking about keeping it around for inventory, and possibly scheduled household like changing furnace filters, smoke alarm batteries, winterizing lawn equipment, etc.
Not ALL ERP systems are big and complicated. It's like configuration management, it's only as complicated as you need it to be.
It's even open source if you wanted to trial it out.