The verb, to long, first appears in what is now a recognisable but obsolete form:
OED
II. Senses relating to emotional or physical condition.
†4. transitive (impersonal). me (etc.) longs (also longeth): I (you, etc.) have a yearning desire; I (you, etc.) wish earnestly.
Usually with after, to, or infinitive.
eOE tr. Orosius Historiarum adversum paganos libri septem . (BL
Add.) (1980) ii. v. 48 Hu lustbærlice tida on ðæm dagum wæron..þæt
us nu æfter swelcum longian mæge swelce þa wæron.
The quote dates from somewhere around 890 AD.
In its current form, it appears 300 years later.
6.a. intransitive. With for (also †after, occasionally †at, †to) or infinitive. To have a yearning desire or strong wish for
something; to yearn to do something.
c1225 (▸?c1200) St. Katherine (Royal) (1981) l. 724 Þe
cwen..longede forto seon þis meiden. [The queen longed to see this
young woman]
As a count noun longing appears around 1000 AD
2.a. The condition or fact of feeling strong desire; yearning.
OE (c.1000 AD) Seafarer 47 A hafað longunge se þe on lagu
fundað.
There is then a significant gap in the development of the root. As an adjective, longing is first recorded in the early 15th century.
2. That longs for something or someone; characterized by strong desire or yearning.
a1425 (▸?a1400) Cloud of Unknowing (Harl. 674) (1944) 26 Smyte
apon þat þicke cloude of vnknowying wiþ a scharp darte of longing
loue.
The adverb, longingly, is recorded 10 years later:
1435 R. Misyn tr. R. Rolle Fire of Love 103 Longyngly in lufe
dee.
And its etymology is given as
Etymology: < longing adj.1 + -ly suffix2.
In manner characterized by longing; with strong yearning or desire.
Given the time between the verb and noun and those and the adjective/adverb, the conclusion of the OED on the etymology of “longingly” seems to be justified.
The progress thus seems to be verb -> noun -> adjective -> adverb.