The answer is easier than you think
Functional words and phrases are whatever that client needs them to be, at that time and setting.
There is no set of words/phrases that automatically applies to each person with aphasia. Figuring out what words and phrases DO apply should be relatively easy with some family participation.
If I'm the person with aphasia, it means that there are certain words and phrases that apply to me but maybe not to someone else. I may not have a cane, but I may have a pet raccoon. Therefore, "cane" isn't important for me to say or communicate, but "raccoon" is relevant.
There can be fine lines between functional, relevant speech and learning common household items. For example, does someone really need to say "spoon"? How often do you talk about spoons? It happens occasionally, but in general, there's always silverware on the table or accessible already. Saying 'spoon' rarely comes up in everyday life—it's mostly used to get a client to initiate speech. So is working on the word 'spoon' a good use of your time?
The time and setting need to be taken into consideration. When the client is still in the hospital, they may just need to understand or communicate 'pain', 'doctor', 'wife/husband/partner', 'tired', food concepts, etc. Simply saying 'hi' or 'thank you' or 'shut up' can be a big thing. Sometimes people with aphasia want to be able to use their favorite swear words again!
Early in the recovery process, the client may need 'help', 'water', 'bathroom', family names, 'doctor', etc. These are basic concepts that don't even begin to help with the complex thoughts or ideas the client may have, but it can be a starting place to initiate speech or help their understanding. The idea is not to think up every conceivable thing the client may wish to talk about at that time.
Keep it simple, practice it, use it in real life. "Good morning" or 'how are you?" or "what?" may be useful phrases at this time. It's frustrating to be unable to communicate complex thoughts or detailed conversations, but functional words/phrases is part of the overall communication improvement process.
In the nursing home setting, the environment and what the client needs may be more limited. There's a therapy philosophy that since the setting is very limited, the client doesn't need a lot of expressive communication skills. In this setting, the client's functional words may be family names, 'phone', 'tv', 'nurse', 'help', 'no', etc.
Later in the recovery process, functional words may be family names and family concepts, things to do with work or hobbies, tv shows, social exchanges, restaurant ordering phrases, food concepts, etc.
Functional words and phrases are different for each person and may change in different settings and times in recovery. Functional therapy words and concepts should relate specifically to that person and not random object labels. Each person with aphasia has specific things they want to say or write, such as a child's name. These are functional words and are the targets for not just therapy time, but in everyday life.