This is a great question!
And infact, it's the first time I've read a 'young person' make this statement. Generally this is a complaint I hear, and I guess probably most people have heard from their 'local grumpy old man'**.
Youths are lazy!, Youths have no respect for their employees anymore, no loyality, blah blah blah.
This is called job-hopping, or ...
IMHO, it depends on your current financial state,
Can you turn around and leave in case your discussion will go wrong?
In any event, i would talk to boss as soon as i have the change, mentioning exactly what you mentioned, that new project even lower on the grade that you started with and promotion plans.
Location can also play a role, some places will not ...
Then bring it up with your boss. Either he is OK with giving you the promotion that you discussed and you get what you wanted, or he is NOT OK with the promotion, in which case you'd rather find out sooner instead of wasting a few years in a junior position you don't want. Bring up your concerns in a calm manner.
I would go down the route of;
I applied for a more senior role, and was told that as long as I proved capable within the first few months I would be quickly promoted, can I please have some feedback on how you think I am doing and if there is anything I need to focus on specifically to help obtain the senior position as discussed
I think that you made a blunder by trusting an promise without any kind of written statements to back that up. They can simply bow out of these promises and string you along. Making promises about promotions seems extremely risky to me, since they don't even know how good you actually are.
Why do I think so? My manager encourages me to "experiment" with ...
Yep, bring it up now. If they set you up name tag or ID, set you up an e-mail address or other logins or accounts for company systems, they'll typically be only too happy to use your preferred name now rather than changing it later. That said, everywhere I've worked coworkers tend to pick up each other's nicknames pretty fast anyway.