Okay, here's the current list of known craft, now including the Shipyards: Starfleet Ships 2294 - The Future and DSC: Wonderlands tidbits:
Future Starfleet ships of Star Trek: Discovery (31st – 32nd century)
1. USS Discovery (NCC-1031-A, Crossfield class), active (3189)
2. USS Tikhov (NCC-1067-M, seed-vault ship), active (3189)
3. USS Excalibur (NCC-1664-M, Constitution class), active (3189)
4. USS Yelchin (NCC-4774-E, Black Box #1), destroyed (3069)
5. USS Voyager (NCC-74656-J, Intrepid (Janeway) class), active (3189)
6. KSF Khi’eth (KSF- 971014, Kelpien research vessel), wrecked (3064)
7. USS Armstrong (NCC-317856, Constitution class), active (3189)
8. USS Giacconi (NCC-316608, Black Box #3), destroyed (3069)
9. USS Noble (NCC-325002, Constitution class), active (3189)
10. USS Dresselhaus (NCC-325019, Dresselhaus type), active (3189)
11. USS Le Guin (NCC-325060, Mars class), active (3189)
12. USS Maathai (NCC-325023, Angelou class), active (3189)
13. USS Annan (NCC-325051, Saturn class), active (3189)
14. USS Jubayr (NCC-325068, Courage class), active (3189)
15. USS Nog (NCC-325070, Eisenberg class), active (3189)
16. USS Hansando (NCC-325072, Courage class), active (3189)
17. USS Song (NCC-325084, Courage class), active (3189)
Unknown registry number:
18. USS Curie (NCC-…, Curie type), active (3189)
19. USS Cuyahoga (NCC-…, Constitution class), active (3189)
20. USS Coloma (NCC-…, mining vessel), active (3189)
21. USS Gav’Nor (NCC-…, unknown, Black Box #2), destroyed (3069)
22. USS Hiraga Gennai (NCC-…, unknown), destroyed (3064)
23. USS Liu Cixin (NCC-…, unknown), active (3189)
24. USS Maryam Mirzakhani (NCC-…, science vessel), destroyed (3064)
25. USS Thant (NCC-…, unknown), active (3189)
26. SS Foresight (civilian emergency transport), active (3189)
27. Wanderer class
28. Nirvana-class flyer Alice (Burnham’s courier ship)