Hans Engelmann was a prolific composer of light salon music common in American households of the early 20th century. This piece is a sentimental, expressive work focusing on melody and accompaniment texture.
The primary challenge is balancing the singing melody against the undulating arpeggiated accompaniment.
Comparable difficulty and character — good candidates for what to learn next.
Awakening (Op.620 No.2) is rated Henle level 3 of 9 — late beginner repertoire, roughly ABRSM grades 4–5. In the RCM system it corresponds to about level 3.
You should be comfortable at Henle level 3 — meaning you can already play level 2–3 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of Awakening (Op.620 No.2) lasts about 4 minutes.
Awakening (Op.620 No.2) is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include Bohemian Melody by William Vincent Wallace, Berceuse by Laura Netzel, Blumengruss by Wilhelm Lege — see the full similar-pieces list on this page.