Disclaimer: I am not a Spanish speaker, nor have I studied Spanish to any real extent. (I've done some self-study via textbooks and online apps/websites like Duolingo.) However, I know a bit about Spanish pronunciation/phonetics because I'm interested in linguistics and I have read some articles or web pages about it.
Spanish has many cases where the pronunciation of the end of a word changes based on the sound at the start of the following word (or vice versa). But my understanding is that the processes involved are usually not particularly similar to French liaison; rather, in most cases, the Spanish pronunciation phenomena could be thought of as "allophonic" processes.
As you've said in your question, French "liaison" is a very specific phenomenon that clearly involves phonological processes, and is not just a matter of allophony. For example, Wikipedia gives the example of "premier étage", where /ʁ/ is pronounced, even though there is no general rule of French pronunciation that absolutely prohibits vowel-vowel sequences like /ee/ (as in "crée") or /ɛe/ (as in "beignet épicé"). And this contrasts with the pronunciation of a phrase like "premier vol", where there is no /ʁ/, even though the sequence /ʁv/ is allowed in French (as in "servir").
###Phonologically conditioned allomorphy in Spanish
There are a few cases in Spanish of words having special phonological forms conditioned by the form of another word: for example, the definite article typically takes the form "el" when it comes directly before a feminine noun starting with a stressed /a/ sound, but "la" before other feminine nouns. But as far as I know, this kind of thing is quite rare in Spanish. Interestingly, it seems that native speakers tend not to think of this "el" as being just a form of the feminine article; it may "feel" like the masculine article is being used in this context (see the answers to the following question for more details: Why is "agua" masculine in singular form and feminine in plural? "El agua" / "Las aguas" ¿Por qué decimos "el agua" si es una palabra femenina?).
Another somewhat example that I found described in this document ("There is phonologically-conditioned, but not melody-conditioned allophony"), by Tobias Scheer) is the dissimilation of the conjunction "y" /i/ to "e" before words starting with the sound /i/ and of "o" to "u" before words starting with the sound /u/.
###Synalepha
One thing that does occur in Spanish especially at word boundaries is " synalepha": two adjacent vowels across word boundaries tend to be pronounced in the same syllable. Vowels in this context apparently behave differently from word-internal vowels in hiatus, so I think we do have to mention word boundaries in the formulation of this rule.
###Phrase-level allophony
Aside from this, many allophonic processes in Spanish apply at the (prosodic) phrase level rather than at the word level, including the allophony of "d" that you mentioned. See guifa's answer to How should I pronounce the Spanish consonant 'd'?
My understanding is that the allophony of "b/v" and "g" follows the same general pattern: approximant or fricative allophones are used between vowels and plosive allophones are used phrase-initially or after the coda nasal. (In other consonant-consonant sequences, the rules are a little bit more complicated: for example, I have read that the heterorganic sequences "lb/lv" and "lg" are pronounced with approximant allophones, but the homorganic sequence "ld" is pronounced with the plosive allophone of /d/.)
Many parts of Spanish pronunciation vary by dialect, however, so I don't know if it's possible to give a comprehensive description of the processes that may apply. For example, the coda nasal assimilates in place to a following consonant across word boundaries in many dialects, but in others I believe it is always velar [ŋ]. I also found an abstract of an article here that talks about dialect differences in the realization of "d", "b/v" and "g" after other consonants.
I don't know too much about this following topic, but the "aspiration" of word-final /s/ is I believe another area where pronunciation may vary based on the following sound.