A little more on the issue of Germany. It appears that there was quite a tradition of Bavarian pedlars (often women) spending the summer in England selling brooms and other wares; in the winter they went back home to stock up again. It seems reasonable to guess that that is what happens here; there's no need to look for some "recruiting" sub-text. As Pavane pointed out earlier, this particular kind of broom was typically a light duster or fly-brush, rather than the quite different besom (also frequently made from broom) of Buy Broom Buzzems.

By way of illustration, The Bavarian Girl's Song or Buy a Broom was a popular stage song of the 1820s or so, being regularly re-published in various forms (localised to America or Boston in some cases) and with various claims as to authorship. There were other Buy a Broom songs, too, but this particular one made it into tradition, at least for a while. The Roud Index has it at number 13229. The following is taken from sheet music at The Lester Levy Sheet Music Collection:

BAVARIAN GIRL'S SONG (BUY A BROOM)

(The Words by D.O. Meara. Arranged by Alexander Lee.)

From Teutschland I come with my light wares all laden,
To dear happy England in summer's gay bloom,
Then listen fair Lady and young pretty maiden
Oh! buy of the wand'ring Bavarian a broom.

Buy a Broom, Buy a Broom
[Spoken] Buy a Broom;
Oh! buy of the wand'ring Bavarian a broom.

To brush away insects that sometimes annoy you,
You'll find it quite handy to use night and day,
And what better exercise pray can employ you,
Than to sweep all vexatious intruders away.

Buy a Broom, Buy a Broom
[Spoken] Buy a Broom;
And sweep all vexatious intruders away.

Ere winter comes on for sweet Home seen departing,
My toils for your favor again I'll resume
And while gratitudes tear in my eyelid is starting,
Bless the time that in England I cried Buy a Broom.

Buy a Broom, Buy a Broom
[Spoken] Buy a Broom;
Bless the time that in England I cried Buy a Broom.

[Spoken] Ye, I shall go back to my own Country and tell them there I sold all my wares in England... singing

[A snatch of Lieber Augustin follows].

The whole can be seen at Levy: The Bavarian Girl's Song. Buy a Broom. (English and German)   The Words by D.O. Meara. Arranged by Alexander Lee. Published by E.S. Mesier, Wall St. & Broadway; no date. Sung (In Character) by Madame Vestris, With the most enthusiastic Applause.

There is another issue dated 1827. Madame Vestris (1797-1856) was a celebrated contralto.