Illinois and Connecticut had suburbs that leaned GOP. However after the GOP drifted rightward on social and religious issues, combined with immigration and a growing minority population they become democratic leaning. Bill Clinton won these states by changing some stances on economic issues . Instead of raising taxes on everybody aka: Mondale 1984. it became lowering taxes for the middle class and raising them on the wealthy. This allowed the democrats to win white suburbanites in states like Illinois and Connecticut which previously were strongly GOP leaning.
Vermont is an interesting case of a state without much immigration as those other states but shifted towards the Democrats. But its the same social factors with many in vermont disagreeing with the rightward social shift of the GOP after the 1970s growth of evangelicals participation in politics when before they either didnt vote or didnt vote based on social/religious issues, that made the GOP become a socially evangelical minded party to capture those voters.
Plus vermont had influx of out of state residents in North-East that brought with them a more left leaning minded politics.
https://www.nytimes.com/interactive/2014/08/13/upshot/where-people-in-each-state-were-born.html#Vermontin 1960 27% of vermonters were born in another state. by 2010s it was 48%.
As for why vermont didnt go democrat until 1992. Vermont benefited from the 80s economic growth that was credited to Reagan and that made the GOP win the state in 1984 and 1988 much less strongly as those Anderson voters who voted for Reagan in 1984 started switching to the democrats. Then the state was hit in the 1992 recession which allowed for Bill Clinton to win a plurality. And when the economy was in good shape by 1996 a lot of voters that once voted GOP decided that they liked the Democrats better and joined with the growing liberal base in the state made it strongly democratic leaning after 1992.