Operate under the assumption of semi-linear merges?
Gitlab has a very cool (and helpful) feature called "Merge commit with semi-linear history":

In practice, in order for a MR to be merged, it must be first contain all commits of the target branch (via rebase or merge).
This guarantees that the CI run for the MR source branch is going to lead to a green build also when merged in the target branch.
The problem is that dependabot-script generates dozens of dependency upgrade MRs (which is fine), and each merge requires a full rebase of all other MRs. The question is whether dependabot-script can somehow rebase those, or react to triggers on merge, so that its open MRs are rebased automatically.
Is something like that feasible?
Before using Dependabot with our Gitlab we tried Renovate.
When their script creates an MR it offers you the option (a todo checkbox in the MR description) to rebase. It also offers several settings for Updating and Rebasing Branches.
On a slightly different approach, it can also group MRs and allows different rules based on Major vs Minor updates.
Send feedback to Github and ask for this feature: https://support.github.com/contact/feedback?category=prs-and-code-review
If more people ask it's more likely they'll add it.
It's already built into Gitlab, Azure Pipelines and others.
https://github.community/t/feature-request-semi-linear-history-merging-strategy/2325