Unless your carrier is using any eSIM features not available in modern SIM cards (6 to 8 years ago should still be the same) or if the card you have was a 3G/4G-specific one, nope, it should not affect your reception.
Your signal strength is completely dependent on the phone's hardware and the SIM card can only affect how your carrier handles the connection. Now, if the carrier is de-prioritizing you because of an older card, then that is completely up to your carrier. Your carrier should be able to tell you if your current card can still access all of their network features and, if not the case, able to offer a replacement.
That being said, it is recommended to switch to eSIM at some point since that's where all future phones are gearing towards. If you don't have any data in your SIM card (like contacts), then it just makes one less piece of hardware to handle if you can switch.