history - progressive forms: participle or gerund?

Progressive forms of verbs consist of the form to be + participle. At least that is what most English grammars say or they are imprecise and speak of the -ing form. My question is what follows after the forms of to be?

I'm working in the garden.

Is working here a present participle or rather a gerund?
I asked myself this question long after I had left school, simply because one accepts what grammar books say without much reflection. But the longer I think about this problem, the more I tend to see it as a gerund.

I stumbled upon this through a curious way of speaking in German dialects. Normally we don't use progressive forms in German, but some dialects make extensive use of forms such as

• Ich bin am Aufräumen - word-for-word translation: “I'm at tidying up”.

Normally in English a preposition such as in "at tidying up" is omitted and it becomes:

• I'm tidying up.

On another forum, a German language one, we noted the German dialects that made extensive use of such forms as beim/am Aufräumen—and we discovered that these forms are used extensively in areas along the River Rhine from Switzerland to the north, but also in the east of Germany and in the south. So it is reasonable to ask what form is used in English, participle or gerund? In German it is a gerund, a participle would be unusual. So it might be the same in English, but since participles and gerunds have the same form, it is really difficult to decide which form it is.

I derive the progressive forms from a formula with "in the act of doing":

• I'm working in the garden means “I'm in the act of working in the garden.”

When you omit "in the act of" you get the normal progressive form.

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I forgot to mention that the following archaic form also exist

We were ahunting / went ahunting

where one may assume that the prefix a- is a relic of a preposition.