Salaam almarhom,
I believe that Salat al-Wusta is most likely Salat al-Asr.
This tradition seems to have made its way to the hadiths, as there is even a hadith that places special weight on the Asr prayer.
Every week there is a topic about salah, and until now I haven't seen a study of all the verses together as I did some time ago
here:PRAYERS SO FAR:
1. Pray during the night, specifically the first part of the night (al-layli) (73:1-7)
2. When you wake up (7eena taquum) (52:48-49)
3. During the night (min al-layli) (52:48-49)
4. At Dawn (At the retreat of the stars - adbaar al-nujoom) (52:48-49)
5. In the morning (bukratan) (76:25-26)
6. In the evening (aseela) (76:25-26)
7. And a part of the night (min al-layli) (76:25-26)
8. Before the rising of the sun (qabla tuloo3 al-shamsi) (50:39-40)
9. Before the setting of the sun (qabla 'l-ghuroob) (50:39-40)
10. During the night (min al-layli) (50:39-40)
11. During the night (min al-layli) (51:16-18)
12. In the early dawn (bil-as7aari - su7oor) (51:16-18)
13. Before the rising of the sun (qabla tuloo3 al-shamsi) (20:130)
14. Before the setting of the sun (qabla ghuroobihaa) (20:130)
15. During the night (min 2aanaa2 al-layli) (20:130)
16. At the ends of the day (different from dawn and the evening as they are mentioned in the same verse) (atraaf al-nahaar) (20:130)
17. From the sinking sun to the darkening of the night (dulook il-shamsi ilaa ghasaq al-layli (17:78-79)
18. At dawn (quraan al-fajr) (17:78-79)
19. At night (min al-layli) (17:78-79)
20. In the evening (al-3ashiyyi) (40:55)
21. At dawn (al-ibkaar) (40:55)
22. At two ends of the day (tarafay 'l-nahaari) (11:114)
23. Approaches of the night (zulfan min al-layli) (11:114)
24. In the morning (7eena tusbihuun) (30:17-18)
25. In the afternoon (7eena tumsoon) (30:17-18)
26. At the setting sun (3ashiyyan) (30:17-18)
27. At noon (7eena tudhhiruun) (30:17-18)
28. The middle prayer? (Salat al-wusta) (2:238)
29. A portion of the night (adna min thuluthay al-layli wa-nisfahu wa-thuluthahu) (73:20)
30. At dawn (salat al-fajr) (24:58)
31. At noon (al-dhaheera) (24:58)
32. In the evening (salat al-isha) (24:58)
So to summarize all this information, the salawat prescribed in the Quran are:
1. Dawn - 7eena taquum 52:48-49, adbaar al-nujoom 52:48-49, bukratan 76:25-26, qabla tuloo3 al-shamsi 50:39-40, bil-as7aari 51:16-18, qabla tuloo3 al-shamsi 20:130, atraaf al-nahaar 20:130, quraan al-fajr 17:78-79, al-ibkaar 40:55, 7eena tusbihuun 30:17-18, salat al-fajr 24:58
2. Noon - 7eena tudhhiruun 30:17-18, al-dhaheera 24:58
3. Afternoon - 7eena tumsoon 30:17-18, Salat al-wusta 2:238,
4. Evening - aseela 76:25-26, qabla 'l-ghuroob 50:39-40, qabla ghuroobihaa 20:130, atraaf al-nahaar 20:130, dulook il-shamsi 17:78-79, al-3ashiyyi 40:55, tarafay 'l-nahaari 11:114, 3ashiyyan 30:17-18, salat al-isha 24:58
5. Night - al-layli 73:1-7, min al-layli 52:48-49, min al-layli 76:25-26, min al-layli 50:39-40, min al-layli 51:16-18, min 2aanaa2 al-layli 20:130, ghasaq al-layli 17:78-79, min al-layli 17:78-79, zulfan min al-layli 11:114, adna min al-layli 73:20,