Learn Dutch: De plot is trouwens erg overtuigend. - The plot is very convincing, by the way.

Trouwens means "by the way" or "incidentally". As a structuring adverb, it is used to smoothly add an extra piece of information that supports your overall point or just came to mind. Unlike the English "by the way", which usually sits at the very beginning or end of a sentence, trouwens typically goes in the middle of a Dutch sentence, right after the conjugated verb.

Why does overtuigend end in an -d?

It is the present participle (the "-ing" form) of the verb overtuigen (to convince), formed by adding -d to the infinitive. Here it is used as an adjective meaning "convincing". Because it comes after the verb is rather than directly in front of a noun, it does not get an extra -e at the end.

Could I say heel overtuigend instead of erg overtuigend?

Yes, absolutely. When placed before an adjective to mean "very", erg and heel are completely interchangeable. Erg can sometimes sound slightly more subjective or emphatic, but both are perfectly natural here.

Is plot always a de-word, even though it is an English loanword?