75x Class 150 (2x 150/0, 34x 150/1, 23x 150/2 and 16x 150/9).
7x Class 155.
47x Class 156.
53x Class 158.
16x Class 170.
29x Class 319.
16x Class 333.
Total: 243 units.
In the franchise agreement, it says five 319s are/were due to go off lease once enough 331s are in service, so only 29 would be retained.
The franchise agreement specified 32x 319s, 20 inherited and 12 cascaded, of which 5 were to be returned, so that leaves 27 not 29. 8 of these are being converted to 769s, so a final fleet of 19x 319s + 8x 769s, assuming all the returned units will be 319s not 769s.
The 150 count is complicated by the franchise agreement option to reform 24x 2-car into 16x 3-car, reducing the total unit count by 8. I am unclear what Northern's current intention is regarding reforming.
The franchise agreement specified a total, before reforming, of 80x 150s, comprising 78x 2-car (58 inherited plus 20 cascaded) and 2x cascaded 3-car. 162 individual vehicles versus 168 in your count. With reforming, the franchise agreement unit count could drop to 72, comprising 54x 2-car and 18x 3-car. If your 75 total is correct, there must be 3x 150/2s, not included in your unofficial fleet list, that are yet to arrive. Where will they come from?
For all the other classes, your counts are in line with the franchise agreement. However, the agreement also requires 18x more 2-car refurbished units (170 or equivalent) by the end of 2022.
The franchise agreement therefore specified a total of 238 to 246 refurbished units (depending on how many 150s reformed), increasing to 256 - 264 by 2023.
The Northern Modernising webpage,
https://www.northernrailway.co.uk/corporate/transformation, states 98 new trains and 243 refurbished trains. However, the 98 figure is out of date - it does not include the 3 additional 195s ordered last year. The correct new train count is now 101 (25x 195/0, 33x 195/1, 31x 331/0 and 12x 331/1). Therefore I suspect that the 243 figure may also be out of date.
Edit: Cl150 vehicle count corrected and comment added.