The short answer is no - because we need to use the exact same TS version everywhere and we need to make sure that everyone uses th exact same TS version everywhere, which would be a very high effort project to do, which (frankly) isn't something worth doing to solve for this really rare usecase.

We control the parser, we control one eslint plugin. But there are many other plugins that exist using type information.
Additionally there are many utility packages (like tsutils or @typescript-eslint/type-utils) that are consumed by plugins.

In order to make this world of "consume TS from the file's directory" work we would have to:

1. traverse the disk for every single file being linted in order to find the TS module
   • this is slow and will kill lint times - disk ops are slow!
2. rewrite our infra to use this specific version.
   • doable, just going to be a high cost exercise.
   • would require new lint rules to help prevent regressions.
3. pass that TS instance around from the parser to plugins
   • easy enough, sure, we can pass it via parserServices probs.
4. ensure that every plugin uses that exact TS instance and no other one.
   • now this is a massive breaking change and something that's going to be really, really hard to enforce.
5. rewrite every utility package so that it accepts its TS module dependency as an argument in some way so that it uses the exact TS instance.
   • impossible to do - util packages just assume they can require('typescript'). Who are we to force them to breaking change their entire API surface?
   • so we fork the utility ecosystem? Very, very high cost and ongoing maintenance cost.
   • tying back to (4) - going to be very hard to enforce everyone only uses utils that respect this world.

Hopefully this helps shed some light on the large complexities that are involved in making the ecosystem work like this.

As I said - the cost is monumentally high and has large ongoing maintenance costs. Such a cost is too great to pay to solve the very, very unique problem.

Generally the solution would be to colocate your linting install and your code install so they have the exact same version. Failing that ensuring that the TS version is synced / enforced via some CI check should be fine.
If you can't colocate but you need the installs to be the exact same physical install, then you're really in a truly unique situation.