Some options.
Types of geodatabases—ArcGIS Pro | Documentation
1. You can continue to use SQL Server Express (free) but you will need to acquire an ArcGIS Server Standard License to have access to the ArcSDE License, that is right ArcSDE License is not sold separate and you need to buy ArcGIS Server Standard, then you can create any number of ArcSDE Geodatabases in SQL Express that you want, you will need to learn more about SQL Server Express and SQL Server Management Studio and the ArcGIS Geoprocessing Tools to create ArcSDE Geodatabases.
2. Move to PostgreSQL (free), also you need to acquire the ArcGIS Server Standard License to get access to the ArcSDE License, then you will be able to create any number of ArcSDE Geodatabases in PostgreSQL that you need, you will have to learn PostgreSQL, psql, pgAdmin, and you can choose esri st_geometry for the spatial geometry type or you can use the PostGIS spatial geometry type to store your data. Therefore, your learning curve might take time, you will need to attend PostgreSQL training and also Esri Enterprise Geodatabase training to better manage ArcSDE Geodatabases, especially when Geodatabase Versioning is involved.
3. You can use Mobile Geodatabases in SQL Lite (free), but be aware that there are Geodatabase functionality limitations, read more in the documentation link below.
Mobile geodatabases—ArcGIS Pro | Documentation
I would say the move to PostgreSQL is your best option, more scalable, and PostgreSQL Geodatabases support all the Geodatabase features and capabilities.
I hope this helps.
| Marcelo Marques | Esri Principal Product Engineer | Cloud & Database Administrator | OCP - Oracle Database Certified Professional | "In 1992, I embarked on my journey with Esri Technology, and since 1997, I have been working with ArcSDE Geodatabases, right from its initial release. Over the past 32 years, my passion for GIS has only grown stronger." | “ I do not fear computers. I fear the lack of them." Isaac Isimov |