“Secession” implies that the North American colonists were fully citizens of the UK; that the North American colonies were fully part of the UK. Both of those implications are obviously wrong.

Did India “secede” from the UK? Rather, India won its independence from the UK and ceased being part of the British Empire.

“Secession” might describe the attempt of Southern States to leave the United States, or the Czech Republic’s successful move to leave Czechoslovakia.

Great read on this is the novel: For Want of a Nail … If Burgoyne Had Won at Saratoga by Robert Sobel, 1973.