SSMS Timeout when browsing for sql servers?
The most likely reason for this is port 1434 UDP being blocked on the new network.

An in-depth analysis of how SQLBrowser messaging works can be found here: https://www.mssqltips.com/sqlservertip/2057/why-listing-all-of-your-sql-servers-does-not-always-work/
That article also lists other reasons for this issue, like the SQLBrowser service not running on the servers, but based on your description of the problem, it looks like the new network you are working on is isolated by a firewall that blocks UDP traffic on port 1434.