Pre- and Post- Snapshot Replication Scripts Not Executing and No Errors
Just a quick summary of some of the things I would try, when analysing the various options....

Have you tried passing the four part object identifier in the scripts?
Instead of using:
... Database.Schema.Table ...

Try using:
... Server.Database.Schema.Table ...

Or in your case where you are using the Linked Server it would be:
... LinkedServerName.Database.Schema.Table ...

Where you define the values as:
LinkedServerName : The name of the linked server as you defined in the Linked Server connection.
Database ........: The name of the database
Schema ..........: The name of the schema
Table ...........: The name of the table

It depends on where the script has to modify data. That's not quite clear in your description, but seeing as you did mention Linked Servers I thought I'd mention it.

The script is executed on the Subscriber as is explained in:

You can specify scripts to execute at the Subscriber before or after the snapshot is applied. Scripts can be used for a variety of reasons, such as creating logins and schemas (object owners) at each Subscriber.

And the additional information provided here is pretty important:

The script is run by launching the sqlcmd utility. Before deploying a script, run it with sqlcmd to ensure it executes as expected. The contents of scripts that are executed before and after the snapshot is applied must be repeatable. For example, if you create a table in the script, you should first check for its existence and take appropriate action if it exists. The script must be repeatable because if you need to reinitialize a subscription for which the script has already been applied, the script will be applied again when the new snapshot is applied during reinitialization.

Reference: Modify Snapshot Initialization Options for SQL Replication (Microsoft | SQL Docs)
If the script doesn't work together with the account that is used for the subscription agent and in conjunction with sqlcmd, then it isn't going to work in the subscription.

Hint
Use ; at the end of every line in the scripts.
Add GO in between lines.


Then you might want to have a look at the article Troubleshooter: Find errors with SQL Server transactional replication. I'm not saying you havent't done that yet, but you didn't say you had. Who knows, maybe you can find the issue in the replication agent's job history...