Is it possible for a coin / token to act as long-term store of value and money at the same time?
Yes. By definition money has to have the following three properties (see Mankiw's Macroeconomics pp 82):
- be a generally accepted means of exchange
- serve as a unit of account
- be a store of value
All these properties are on a spectrum, so something can be less than perfect means of exchange or store of value or unit of account and be called money, but all 3 boxes have to be checked in order for something to be considered money, If something is not store of value, by definition it cannot be money to begin with.
However, you should also note store of value does not mean the money should have greater value over time, it just means it should hold its value without depreciating.
Furthermore, while any money has to be medium of exchange, unit of account and store of value, it does not need to fulfil these roles perfectly to be considered money.
In macroeconomics, there is a concept of narrow money and broad money. Narrow money is what a laymen typically thinks of a money, that is coins and notes and demand deposits. Broad money include everything that is included in narrow money plus even various financial assets like bearer bonds, treasuries or other tradable securities. Treasury does not fulfill all three roles as good as cash or demand deposit, but good enough to still check all the 3 required characteristics to be considered money.
Problem with tokens like bitcoin is that they have deflationary bias. The store of value function is defined in terms of not loosing value over time, not gaining it (see Mankiw ibid). Assets that appreciate are not better store of value than something that is just keeping its value without much inflation, like let's say Euro between 2009-2019 when inflation in the eurozone was for all practical purposes 0 (see Eurostat).
In addition, while you are right that if something tends to appreciates in value people will have more incentive to postpone consumption to future, people still have to consume to stay alive, so even having appreciating money would not necessarily render the money unusable as means of exchange (even though this would have some bad effects on an economy but that is outside the scope of this answer to talk about). In past many countries were on gold standard and gold was an excellent store of value, and while today we understand that gold standard was inefficient monetary system it was a system could exist despite of its many flaws and macroeconomic inefficiency. So being good store of value does not mean that asset cannot be money, although its also not required for money to be perfect store of value.
The problem with tokens is not that they are stores of value (they have to be to be money), problem with tokens is that they are not used as a generally accepted means of exchange. In most countries, generally speaking, if you go to store, a store clerk will generally not accept your bitcoin or other tokens as a medium of exchange. No matter how much value they have, you would first have to exchange your token for euros or dollars and then come back to the store to buy what you want (although of course there are exceptions of places that will accept your bitcoin or etherium or dogecoin or whatnot, but they are only very few such places).
