Are NS records for a .com domain stored by the registrar or the .com registry?

Let's say I own example.com, that I bought by ExampleRegistrar.
Let's say that, by default, this registrar uses their own nameservers ns1.exampleregistrar.com, ns2.exampleregistrar.com.

Thus, when a client wants to browse to www.example.com, it probably goes like this:

• root DNS servers looks for .com nameserver
• .com nameserver looks for example.com, it sees ns1.exampleregistrar.com and passes the request to this nameserver
• ns1.exampleregistrar.com looks for www.example.com and finally finds IP 203.0.113.5 which it gives to the client.

Question: how does it work if I configure a custom nameserver ns1.othernameserver.com in the registrar domain's settings?

Does this mean the registry for .com will directly have ns1.othernameserver.com in its database?

Is it correct that, then, any request from a client to www.example.com will never go through any of the registrar's servers?

The registrar essentially just deals with sales and customer interactions, they are not part of the actual live operations from a DNS perspective.
Well, not as part of their role as a registrar, anyway. It's very common that registrar companies also provide DNS hosting services for customer zones, but that is just a case of value-add or upsell of non-registrar services to their customers.

From a registry as well as DNS operational perspective there is no difference functionally if you used registrar-provided nameservers, third party nameservers, your own nameservers, or any mix of these.

In all these cases, the registrar just sends the set of NS records that the registrant has selected (maybe implicitly if you choose to use their DNS hosting services) to the registry and those are published in the TLD zone.