In my solr managed-schema.xml file I added the following:
<copyField source="computedtitle_t" dest="computedtitlecopy_t" />
When I populate-schema from Sitecore, the managed-schema file is overwritten and so are my changes
Is there a patch file on the Sitecore side where I can add this and to what section?
Yes, Sitecore manages the Solr schema for you through the populate-schema function in the Control Panel. This is done via the SchemaPopulateHelper. You can implement your own class, implementing the ISchemaPopulateHelper interface and register it in the config.
A while back, I wrote a generic implementation of this where you can put your entire managed schema as part of the Sitecore config instead. This also allows leveraging from the Sitecore config file patch feature, so that your schema changes can go along with other Sitecore configs if needed.
You can read more about it here: https://mikael.com/2020/10/dealing-with-solr-managed-schema-through-sitecore-config-files/
Here are some more generic info about how Sitecore works with Solr and managed schema: https://mikael.com/2018/01/working-with-content-search-and-solr-in-sitecore-9/
You can use the code here as a starting point: https://github.com/mikaelnet/sitecore-solr-config
Please note that there was a small interface change in Sitecore 9.3 (I think), so the sample code may need some changes for it to work. Also, make sure you start with a managed schema that is equal to the one that's provided with the Sitecore version you're using. There may be a few changes in the default schema between the versions.