A stuck float is definitely a good place to have a first look. In general, you'll be taking the carbs off and giving them a good cleaning. You'll also inspect the floats for cracks and float needles for any wear or damage.
More specifically, taking the carbs off of an 81-82 CB650 can be a bit of a bear until you get familiar with the whole process.
The first thing you'll need is a shop manual, often called a factory service manual. If it isn't listed in the Manuals & Technical Documents section of this sub, then grab a physical copy from Clymer or sit on eBay for one of the original Honda prints.
The second thing you'll need is a #2 JIS screwdriver. This is because the screws all around the carbs look like phillips screws, but they aren't. Using a regular phillips driver will wreck them and make your life miserable. Vessel is the most commonly recommended manufacturer for a good JIS driver.
Lastly, I highly suggest not purchasing any parts until you know what needs to be purchased. There are many carb rebuild kits, and many of them have terrible parts. Always avoid aftermarket jets and floats. Float needles are mostly OK, and bowl gaskets are fine as long as they aren't torn. You will likely need new bowl gaskets, but wait to order until you know if any other parts are needed. I will always suggest replacing the carb boots / insulators because they are usually rock hard and make reinstalling carbs SO MUCH easier if you have new rubber.
Worst case is that you'll need to replace one or more floats and/or one or more float needles in addition to a full cleaning. Get the manual & your JIS driver, follow the steps to remove the carbs, and get them on a workbench. Follow the manual, spray carb cleaner in every single hole you can find.
You'll find that your carbs (VB44A) have press-in slow jets, which makes some people pull their hair out. You can either leave them and try to clean or drill them out & replace with screw-in slow jets. Search YT for some info around this.
Let us know if you have more questions. I've been around these carbs too much, so I'll give whatever help you need.