Short answer
Involve the people who do the work in designing the new processes, give them a clear reason the change helps them, and remove the old workarounds once the new system is live. Adoption follows when the new way is easier than the old one and leaders use it themselves.
I think most adoption problems are really design problems, because if the new system makes someone's daily work harder or adds steps they do not understand, they will find a spreadsheet to get around it, and nobody can blame them for that. So the first key is to bring department users into process design and testing early, which gives them ownership of the result and gives you feedback while it is still cheap to change course.
The second key is communication that answers the question every employee actually has, which is what changes for me and when, and that message works best coming from their own supervisor rather than from a project newsletter. I also like to name super users in each department who get extra training and early access, since people will ask a colleague down the hall long before they open a help ticket.
After go-live, shut down the old system for daily work as soon as it is safe, retire the shadow spreadsheets, and have leadership pull their reports from the new system rather than asking finance to produce them the old way. When managers visibly rely on the new system, everyone else follows, and the Start at Zero Substack has regular notes on what is working for agencies going through this.