You said, "The Declaration of Independence was an announcement to Great Britain that we no longer recognized their authority."
How is that not withdrawing from our former association with England?
An aspect of secession, as illustrated in more depth here: https://en.wikipedia.org/wiki/Secession is identified by the adjective formal - “The act of secession is the formal withdrawal from a union or confederation”.
As in a circumstance such as divorce there is mutuality of terms and purpose between all parties. If you look at the examples at the link you see references to ratifications and negotiated consent.
My point is that there was none of that with the colonialist rebels. It was actually more than just an announcement - it was a throwing down the gauntlet in full recognition of the likely response.
We didn’t simply “withdraw” from British rule - we tore ourselves away from their control. We didn’t secede against their authority - we openly rebelled against it. We didn’t give a damn if they liked it or not - we were beyond “praying for relief” or asking for consideration.