I don't think this necessarily means that expats' hopes of making money from their savings is over - even in the very unlikely event of the AKP actually managing to achieve zero interest. Although I am not an expert in these matters, I understand that the abolition of interest does not mean that you get no return on your capital. What is excluded is that form of return that consists of a fixed return to the depositor over a specified period of time. See NOTE at end). There are many other ways of profiting from financial and other business transactions. For example, here is how Wikipedia describes Wadiah (safekeeping).
In Wadiah, a bank is deemed as a keeper and trustee of funds. A person deposits funds in the bank and the bank guarantees refund of the entire amount of the deposit, or any part of the outstanding amount, when the depositor demands it. The depositor, at the bank's discretion, may be rewarded with Hibah (see above) as a form of appreciation for the use of funds by the bank.
It is not difficult to envisage, for example, Garantibank and Finansbank in rivalry for capital each publishing figures on how generous they have been in appeciating their depositors. From the point of view of the depositor there may be little practical effect. I guess maybe you find out out what return you are getting at the end of a specified period rather than at the start. You might think of it as not being a "customer" of the bank but as a "partner" in their business investment and entitled to get a share of the profits. Islamic banking can be very effective in promoting business. Indeed many people ascribe the success of the "Anatolian Tigers" of Central Anatolia - partially - to this form of banking.
As I say, I am no expert, but it is just as well to remember that the "Western" way of doing things is not the only possibly successful way.
What muddies the water on this is that Erdogan says he is not doing it for Islamic reasons but because people should work for living not live off unearned income. I take this as no more than propaganda appealing to poor people and workers who the AKP presents itself as representing against "the idle rich". An election is coming up.
NOTE: In terms of economic theory, Islamic finance does not accept the doctrine of "the time value of money". Put crudely this is the notion that £1 today is worth more than £1 in the future (this has nothing to do with inflation which is a quite separate matter). This means if you deposit money over time you must be compensated for this. Islamic banking soes not accept this but if yoour bank invests your money and makes a profit then you can share in this. Indeed, why the hell else would you use a bank (other than for safe storage and paying bills). So, you don't get "interest" just for leaving your money in the bank for a month; you do get some form of return if the bank makes a profit in its activities during that month.