No pfsense is not going to be the master browser for the moronic windows network neighborhood.
I would suggest determine who your master browser is.. Here is a simple tool to do that with..
https://scottiestech.info/2009/02/14/how-to-determine-the-master-browser-in-a-windows-workgroup/
Why do you care about the stupid browse list anyway?? Do you not know the name of your NAS? Why do not just access it via is fqdn ie nas.yourdomain.tld ??
But to be clear, unless you installed some samba package on pfsense, it has ZERO to do with participation in maintaining the brwose list. And it being your gateway, it has ZERO to do with broadcast traffic between devices on the same network. You do understand that the browselist can take long time to fully populate. Had you recently turned off machines, say your master browser and now a new election was held, then all the clients have to register themselves with the master browser, etc. etc..
While I do not use that stupid list, I do make sure it works on my network for examples for people that do want to use it ;) What I would suggest is you turn off the computer browser service on all boxes that you do not want to be the master browser. You should pick a box that is on 24/7/365 or as close to that as possible to be your master browser.. For example I have my linux box as my master browser running samba.
$ nbtstat -A 192.168.9.7
Ethernet:
Node IpAddress: [0.0.0.0] Scope Id: []
Host not found.
Local:
Node IpAddress: [192.168.9.100] Scope Id: []
NetBIOS Remote Machine Name Table
Name Type Status
–-------------------------------------------
UBUNTU <00> UNIQUE Registered
UBUNTU <03> UNIQUE Registered
UBUNTU <20> UNIQUE Registered
☻MSBROWSE☻<01> GROUP Registered
LOCAL <00> GROUP Registered
LOCAL <1D> UNIQUE Registered
LOCAL <1E> GROUP Registered