would the government be able to find out that I own the anonymous e-sim on it if my other sim in my phone is another provider not silent-link

Yes. They can almost certainly tie the hardware ID (IMEI) of your phone to your identity through your non-anonymous service provider, and probably do through mass surveillance programs. Whether that's a security problem for you depends on what you're doing with it; surely you aren't using SMS, standard phone calls, or unencrypted messaging services for anything you really want to keep private.

If you want phone service that will resist targeted surveillance by local authorities, even routinely turning on the cellular modem where you live, work, or study is a risk. This article detailing one person's approach to securing a phone was posted to Lemmy today and should give you a clue about the possible threat models.

I just know one thing, if it's advertised as an anonymous solution there is a bigger chance to be monitored by LEA.

Pay with Monero, set up a VPN, buy a phone specifically for the service. I doubt you can get any more anonymous than that. Cellular networks are by default monitored by governments, there is nothing a provider can do about it. But encrypting the traffic and getting a new phone should make that type of monitoring relatively useless. And if you never give your identity to the provider, they simply can't know who you are.