With the caveat that I am not a linguist nor an expert on this:

While the derivation from the Latin "uti" is correct, to your question as to whether "use" was an abbreviation of "utilize", the answer per my reading of the OED is "no."

They trace the etymology of "use" back to the latine "uti" as follows:

< Anglo-Norman usere, usser, huser, auser, Anglo-Norman and Old French, Middle French user (French user ) to spend (a period of time) (c1100), to utilize (something), to follow, observe (a law or custom) (first half of the 12th cent.), to exercise, practise (a trade, a skill), to deteriorate, wear out, to eat, consume (food), to become familiar with (something) through habit, (with infinitive) to be accustomed to (all second half of the 12th cent.), to frequent (a place), to perform (an act, a miracle, etc.) (both early 13th cent.), to wear (clothes), to wear (something) out, damage (something) through use, to act in a certain way according to custom, to have sexual intercourse (with) (all second half of the 13th cent.), to speak (late 15th cent. in user de beau langaige , user de grant rhetorique ) and its etymon post-classical Latin usare (also usuare) to observe (7th cent.), to enjoy (8th cent.), to wear out (9th cent.) classical Latin ūs- , past participial stem of ūtī to make use of, put to use, to take, consume (food or drink), to wear (clothes), to live or spend time in (a place), to employ (words, language) in speaking, to employ (a person), to manage, handle, control, to engage in, practise, to conduct relations with, treat, to have sexual intercourse with, to experience, undergo, enjoy, in post-classical Latin also to be accustomed to (c1290, c1451 in British sources), of uncertain origin. Compare Catalan usar (1272), Spanish usar (c1200), Portuguese usar (13th cent.), Italian usare (late 13th cent.). Compare use n. That classical Latin ūtī originally had a diphthong in the first syllable is indicated by the forms oeti , oetier for ūtī , and oitile for ūtile in early inscriptions and legal texts, and an Italic origin is indicated by Oscan úittiuf (nominative) use, Paelignian oisa (ablative singular feminine) used.

By contrast, "utile" is from the derived latin form of uti: "utilis".

"Utilize" doesn't exist as construction in romance languages (or in English) until much later:

French utiliser (1792), < Italian utilizzare (1760), < utile utile adj.: see -ize suffix, and compare Spanish utilizar, Portuguese -isar.

Their earliest recorded usage for "utilize" in English is 1807 and notes that:

Rare before 1858. ‘Utilize is fast antiquating improve, in the sense of “turn to account”’ (1873 F. Hall Mod. Eng. 167).

By contrast, the earliest English citations for "use" are medieval:

"a1250 Lofsong Lefdi (Nero) in R. Morris Old Eng. Homilies (1868) 1st Ser. 207 (MED): Ich halsi þe þet ðu bi-seche him..þurh alle þe oðre sacremenz þet holi chirche foluweð and useð."

As to whether or not "uti" was slang in Latin is beyond my knowledge or ability to look this kind of thing up.

Might be worth posting this to r/linguistics (although take note of their rules on Q&A threads) and r/latin.