शब्दानुशासनम् व्याकरणम् । The science of sound is Vyakaranam.
संप्रत्ययः शब्दः । ध्वानिः शब्दः - इति महाभाष्ये - both knowledge (meaning) and the original "sound" is associated with "Sabda" in Samskrit. The sound is given more importance in Samskrit lanaguage than the word (पदम्) as the natural sound in itself has inheritted meaning with it. The "word" being its derivative added with a suffix, conveys the derived /modified meaning of the original sound. Thus the language is also its derivative. However vyakarana is made to convey the meaning grammar - it is more than just grammar, as vyaakarana deals with all the derivations of the primordial sounds such as - words, word-sense, phrases, sentenses, figures of speech, etc. (यद्यपि पदशास्त्रम् इति विश्रुतं तथापि शब्दसाधुत्वासादुत्वविषयैव अस्य वेदाङ्गस्य महत्वम् इति). The shaastra that deals with 'sound' in its basic form is called as Shikshaa (शिक्षा) which is primarily a Vedanga (a part of Veda like Vyaakarana)
Shikshaa (शिक्षाशास्त्रम्) shaastra is the foundation for studying the 2 branches of Samskrit language (भाषा नाम संस्कृतं - वैदिकं लौकिकञ्च) Vaidika (Vedic Samskrit) and Laukika (Classical Samskrit) - Laukika is the part of language that is in use for all purposes other than Vedic - including Science, Literature, Medicine, and all other worldly things.
Shikshaa (शिक्षा) shaastra in its full form is a complex and intricate science based on human vocal system. Which in its full capacity in use in Vedic part of Samskrit (वैदिकसंस्कृतं). The same shaastra is also used in a limited manner in the all purpose non-Vedic part of Samskrit (लौकिकसंस्कृतं).
Even though Sandhi (सन्धिः) is studied along with Grammar, Sandhi deals only with the pronunciation of syllable (Varna वर्णः) with respect to the factors such as - Place (स्थानम्), Effort (प्रयत्नम्), Duration (मात्रा), Pitch (स्वरः), etc. (स्थानादयः). All these deals with Syllabicity (syllables) and phonological aspects (which are part of Shikshaa) than words and meanings. Thus Sandhi is primarily a subject of Shikshaa than grammatical processes - even though Sandhi rules are given in grammar texts (व्याकरणम्), however the place, etc. (स्थानादयः) are elaborated in 'Varnochaarana shikshaa' and 'Paniniya Shiksha' of Maharishi Panini. The rules for changing of syllables based on enjoining of syllables, though found in Grammar texts but are in essence part of the Shikshaa /Phonology.
Thus the linguistics treatise Ashtaadyayi not only deals with Grammar (which is primarily Syntax & Semantics - विभक्तिः कारकम् च) it also deals with the rules of Phonetics - Shikshaa and in general all aspects of "Sound" (शब्दः) which forms the basis for language - including morphology, etc.
Not just Sandhi, the fundamental formations in Sanskrit Roots + Suffixes (प्रकृतिः + प्रत्ययः) and the word generation (व्युत्पत्तिः) processes essentially are based on phonetics (शिक्षा) like Vriddhi, Guna, Samprasaaranam etc. (वृद्धिः गुण सम्प्रसारणम् इत्यादिप्रक्रियाः) - Process of expansions of syllables which purely natural sound modifications while joining syllables. These are evident across word formations - in both Noun forms and Verb forms from singular to plural forms and also declensions. The Vriddhi, Guna, etc. part in primary and secondary Noun derivatives from Noun roots, Nouns and Verb roots, etc. (वृद्धिगुणादयः - कृत्तद्धितेषु) are again strictly follow the rules of phonetics. In addition the the phonetic features such as Natvam, Shatvam (णत्वम् षत्वम् उभयमपि) are also part of shikshaa. Also the letter 'h' (ह्) becoming the forth letter of the group consonents (वर्गीयचतुर्तम् अक्षरम्) are again shikshaa. Similarly all most all the Dhaatus (निज-धातुः) - Verbal roots are also single syllable phonetic (sound) forms - also the suffixes (प्रत्ययः). The prefixes (उपसर्गः) are again mostly dual syllable sound forms.
There are many shikshaa shaastras (शिक्षाशास्त्राणि) more than 40 so far we have got for Four Vedas (चतुर्वेदाः) and their shaakhaas. Of these Paniniya shikshaa for Laukika (non-vedic) branch of Samskrit is famous. Thus Maharishi Panini integrated all these branches of 'the science of language" in his monumental work Ashtaadyayi. It appears that the entire work of Maharishi Panini is to make rules for pronouncing the "Word" correctly as the "Word" in itself has the inseperable meaning attached with it - thus the perfect pronunciation of just one "Word" takes you to heaven as per Maharishi Patanjali.
The word "vyaakaranam - vi+aa+kr+lyut (suffix)" (व्याकरणम् = वि+आ+कृ+ल्युट्) itself means a "Special form" (of language) - with stress on the verb (creation of the form), the other 2 similar words (1)"aakaarah - aa+kr+ghan (suffix)" (आ+कृ+घञ्) and (2)"aakritih - aa+kr+ktin (suffix)" (आ+कृ+क्तिन्) both represent form and shape respectively in common usage. The extra 'vi' (वि उपसर्गः) prefix gives the meaning of Special. Thus the word vyaakaranam itself means the entire science of the creation of the language. Which includes abiding by the natural phonetic capabilities of human vocal faculties and also reflecting the natural and eternal "sound-meaning" combination (शब्दार्थयोः निसर्गनित्यसम्बन्धत्वम्).
The entire Shikshaa shaastram is based on Human vocal anatomy and its primary purpose in laukika part of language - is to make pronunciation easy and natural (similar to Veda) in addition to shortening, softening, replacing, adding, etc. of syllables based on natural movement of tongue and natural functioning of vocal chord. This has also helped in making the entire language musical - which in-turn helped in easy communication and retention of huge volumes of treatises over 1000s of years, generations after generations based on the most natural and easy to remember phonological sounds.
The natural inter-wining of phonology and language - music and literature, - a true Wonder!. Hope we understand, hold it dear (in our tongues) and preserve it by passing to the next generation without any deterioration...
This shikshaa shaastra is primarily a Vedanga - which means a part of Veda... and also used in Yoga, Tantra and Shastras. The natural relationship between Language and Phonology proves that Samskrit is a well constructed (not by human) language and is indeed the greatest gift to mankind, from who? - who else...!
Personally this has lead me to the conclusion that originally all 6 Vedangaas (Shikshaa, Chandas, Nirukta, Vyaakaranam, Jyotisha and Kalpa) must have been a single shaastra (may be called as Vyaakaranam - based on the Yogaartha of the word) and must have been an integral part of Veda in the earlier Era (Dwapara Yuga) where Veda was just one !
Basic details of Shikshaa you can fine here https://vedavichara.com/the-vedas/vedangas-the-limbs-of-vedas.html