Thank you for the detailed explanation :)

Although there is no essential difference in meaning, the usage frequency differs. We are more often likely to use "bog" as in "bog down". Example, "I am so tired, bogged down at work." "The Internet is bogged down with video streaming." Of course bog is a noun also, meaning swamp. "Mired" has a more formal usage and you are more likely to see it in writing than everyday speaking.

According to the dictionary, they're interchangable.

I don't think there is any significant difference between them. They have similar meaning as nouns and also as verb forms (to be mired, to be bogged down).