There is no soft and hard cap.
There is a limit of 5m SP after which Alpha characters stop being able to gain skills via the training queue. That is a cap on training, not SP, as Alphas can still gain SP from other sources (events, log in rewards, injectors).
The commonly cited ‘20m SP “limit”’ is not the maximum SP an Alpha character may have; it is the sum of all the SP that can be applied to skills that Alpha pilots can use based on the individual skill limits for Alpha characters. It’s actually less than 20m SP, based on the SP multiplier data and Alpha limits on EVE Uni - I calculated it as 16,169,810 SP available to Alpha pilots at this time. I wasn’t active when this all rolled out, so I’m not sure if CCP overstated the possible SP or if there have been changes to accessible levels/multipliers over time that dropped this number.
If an Alpha waits to go Omega until they train up to the 5m SP limit, they can max out all the rest of the Alpha-available skills in 5 months as an Omega if they have optimal attributes and +5 implants - even at the highest monthly rate of $15 USD that’s all of $75 - much cheaper than buying 224 Alpha Injectors to fill up the Alpha SP tank (that’s 4480 PLEX for around $160, assuming the player does not buy any excess PLEX, or around $175 if buying the Injectors outright). From there, well, if they want Omega skills/access they really should be paying for the whole game.
Since I was adding things up anyway: total possible assignable SP for an Omega pilot is 445,725,675. At optimal attribute mapping with +5 implants on an Omega clone, that is over 18 years of training (excluding boosters and various sources of free SP). Assuming a player subbed annually but had no other pricing discounts, giving a cost of ~$11 USD per month (annual sub rate), that’s almost $2500 (pre-tax) just in sub costs to reach that total of SP, not accounting for player time, the ISK necessary to get all the skill books (many of which are not seeded on the market), the implants, and the loss of content benefits from having to spend all that time in a training clone. If someone spent 6 hours a day in a non-training clone, that time expands to over 25 years.
EDIT: Ok, not 25 years - I flubbed my calculation there and removed all training for 6 hours a day instead of just implant buffs for 6 hours a day - but still longer than 18 years. I don’t feel like re-doing the math for the exact additional time right now, but I’ll try to remember and edit in the fix tomorrow.
Also, I suppose I should mention that Alpha accounts can acquire SP past 16m, but they are unable to apply it toward Omega skills while in an Alpha state. So one can have an Alpha clone with SP beyond 16m SP and only Alpha skills trained - the rest of the SP would be unallocated SP.