You can get the Shimano bleed cup for $12 and it does everything you need.
You can get various syringe-based ones on amazon for a similar price.
Even if you do, also get the bleed cup. It is handy to have for simple top-offs.
Looks like Shimano now has a new version as well:
https://cyclingtips.com/2021/08/spot...d-tool-review/