May Allah bless you for your patience.
I stated Friday prayer once a week observed between salat el fajr and salat el ishaa is called EL-SALAT-EL-WUSTA.. 2:238 refers to once a week for the following TWO reasons, 1)due to a specific prayer found in 62:9.."when the call to prayer is proclaimed on the "day of gathering/FRIDAY" DROP ALL BUSINESS and hasten to the remembrance of Allah.." this prayer happens during the business hours (thus 24:37 and 30:18 can confirm this time of prayer) HOWEVER 30:18 ALSO makes a point of CONTRAST between two extremes: heavens vs earth, night vs day, and life vs death (30:19). Secondly is the fact of the definate article "EL" before salat AND also before the word wusta, thus this is a specific salat that happens at a specific time and it is certainly UNIQUE AGAIN DUE TO THE DEFINATE ARTICLE "EL" vs "salat-el-fajr & salat-el-ishaa". Thus EL salat EL wusta is ONE OF A KIND.
In regards to 20:130 I MUST revise my answer and say that the SECOND daily prayer is JUST BEFORE SUNSET UNTIL THE SUN ACTUALLY HAS SET, while the morning prayer FAJR is JUST BEFORE SUNRISE UNTIL THE SUN HAS RISEN.
20:130 is describing the salat timing thus:
A."gloryify the Lord before the rising of the sun AND BEFORE ITS SETTING.."
B. "AND FROM PARTS OF THE NIGHT.."
C. "AND AT THE ENDS OF THE DAY.."
Thus this verse is not ADDING salat but FULLY DESCRIBING TWO SALAT WHICH HAVE A CRITERIA:
MUST TAKE PLACE BEFORE RISING OF THE SUN.. BUT WHEN??
MUST TAKE PLACE DURING PARTS OF THE NIGHT..OK SO BEFORE THE SUN RISE AND FROM THE NIGHT..OK BUT THAT STILL DOESN'T SPECIFY EXACTLY WHEN! 2AM IS BEFORE THE SUN RISES AND DURING PARTS OF THE NIGHT SO..
LASTLY, MUST TAKE PLACE DURING THE ENDS OF THE DAY.. THUS we now have an exact time as to WHEN these two salat occur.
11:114: "two ends of the day(notice same phrase as 20:130) and during parts of the night.." (two ends of the day= two prayers one on each end of the day that takes part during/near some stages of "night"
17:78: "at the suns decline until the darkness of night(one prayer) AND QURAN EL FAJR(second prayer).."
thus the two daily prayers take place BEFORE SUNRISE until sunrise(fajr) and BEFORE sunset until the darkenss of night(ishaa prayer), while EL-SALAT-EL-WUSTA takes place once a week during the day on Fridays. The below ref article mainly supports this theory that the two daily salat were originally fajr and asr(before sunset). Their is a hadith in the article below that states someone asked the prophet(pbuh) what should they do since 5 prayers a day were not managable and the prophet was quoted "atleast keep the asrani" they asked what the asrani was and he replied salat before sunrise and the salat before sunset.(page 58)
“ Western scholars have already noticed that according to Muslim sources,
before the five daily prayers became part of the "pillars" of Islam, the
Muslims used to pray only twice a day. Goldziher states that "before the
duty of prayer was extended to five times a day, the Muslims are said to
have observed only two canonical times of prayer: morning and afternoon
... ".1 Other scholars, like Mittwoch, for instance, who studied the
evidence of Muslim sources, maintained that the first two prayers which
the Muslims reportedly used to pray daily were saLat al-fajr (before
sunrise), and salat al- 'isha' (after sunset).' JSAI 10,1987
MORNING AND EVENING PRAYERS IN
And Allah knows best and has the final say.