PSConfig | configuration data and configuration files | Configuration Management library

It's a good choice to split your farm into multiple server roles to have a better performance and failover improvements. However we must take care about the following situations :)

About the search problem - it's required to change the search topology (index partitions, query, content and crawling components, ..) before you stop the services on current server. Probably you had a corrupted index and topology afected during the services on servers switch. In such situations like that I recommend the following steps:

• Add the new server(s);
• Start all the required service instances for search;
• Change the search topology using Powershell (using clone property on cmdlet) and move all required services to the new server(s);
• After validating the changes on new topology, stop the search service instance(s) on wfe server(s);

Take a look at those links:

https://docs.microsoft.com/en-us/sharepoint/search/manage-the-search-topology https://docs.microsoft.com/en-us/sharepoint/search/manage-search-components

If I'm not wrong the 'Microsoft SharePoint Foundation Web Application' is started by default, but you may stop it without any problem (please make sure you don't have a load balance rule that's forwading web requests for this node). It must not cause any problem into your environment.

As you said you had a rule asking 'psconfig to run' and it's already ran when you started 'SharePoint Products Configuration Wizard' to joing the new app server, BUT if there's a cumulative update or product installation pending that required psconfig to run earlier, that may be a problem, for example - Reporting Services, Project Server, or any other update that may require this to run.

Probably you had a pending a PSConfig to run on new or old server by any reason, so it may mislead this setup. The only way to know what's going on is checking on upgrade log file and fix all required stuff and finally.. run the PSConfig ;)

Answer your last answer - We can clean the new server from the feature it copied from the previous trial (before the removal from the farm)?

It's not a good choice to copy or clone SharePoint servers, because you have a bunch of references locally and on SharePoint Databases (hi SharePoint_Config!).

At this point I recommend you to make sure both of servers are at the same build, considering Operating System, .NetFramework, KBs and SharePoint Service Pack and related build.

After all I suggest you to garantee that your new application server is not joined at the farm anymore (you can do it on manage servers on CA), to make sure you don't have old references, and them running Config Wizard at the first one web front end, to ensure you don't have pending changes to be applied at the farm level, and for last step, join the brand new app server to the farm with all same configuration. You may use powershell or wizard, no problems ;)

Good luck!