Here is what Healthline has to say about Mullein as a supplement:
https://www.healthline.com/health/mullein-leaf#herbal-supplement-risks
It has a number of antibacterial and anti-inflammatory properties, but it has not been shown to be effective against mycobacteria, and there are limited studies about it.

In choosing herbal tonics and supplements, remember that these are not tested or approved by the FDA or USDA, so it is "buyer beware". Look for supplements that:
1) List ALL ingredients, including fillers. Remember, multiple names - common, scientific, ayurvedic, and patent - can be used. If you see an unfamiliar ingredient, look it up to be sure it is not something that your are allergic to or that may interact with other things you take.
2) List the quantity of each ingredient in each recommended dose. Often, cheap filler prevail and only miniscule amounts of the herb you need are there.
3) Carry an independent certification label on the product your are buying - not just say on the website "independently tested" or "purity tested." USP (US Pharmacoepia Convention) or CGMP (Current Good Mnaufacturing Processes) are two labels, and should be on the package. Some distributors certify only a few of their products, othere they just resell from other sources.
4) If possible, by single-herb preparations, at least to start with. That way, if you have a reaction, you will know what ccused it.