The existing answers have mostly addressed your question, but just for posterity, I want to clarify a couple things.
You have to be careful with dBi, as it is not equivalent to total radiated power. Different antennas can have drastically different efficiencies.
What dBi tells you is the peak gain out of all possible directions when compared to a perfect antenna that radiates uniformly and omnidirectionally (isotropic). You should also note that this is a ratio, and that it is on the logarithmic scale, so 3 dB is 2 times more, whereas 20 dB is 100 times more (and the i in dBi means isotropic).
Anyway, the important thing to realize is that a 2.2 dBi antenna could have terrible gain in every direction except for what it is directly pointed at (a narrow beamwidth) and actually be radiating less total power than an omnidirectional antenna.*
When you are in line-of-sight (LOS) environments this peak gain is probably all that matters, as long as the antenna is in fact correctly pointed at the other antenna.** However, in indoor and non-line-of-sight (NLOS) environments, you can get a huge amount of multipath which will create crazy interference patterns -- the signal will bounce off the floors, ceilings, your refrigerator, your phone, etc., and depending on where you are these different reflections can add constructively or destructively, giving you drastically different received power. In these NLOS environments the efficiency of the antenna (total radiated power) often matters a lot more than the directivity (dBi).
* For example, a perfect 3 dBi antenna (2x gain) would radiate all of its power in 180 degrees, both azimuth and elevation (think half of a sphere). This is never achievable in reality, as it is always a gradual change in gain (notably, when you look at beam patterns they typically draw the 3 dB line, a heatmap would show a gradual change). However an antenna that achieved a 3 dBi gain in just an 18 degree beamwidth would also be considered a 3 dBi antenna, even though it is radiating 1/100th the power (since it is 1/10th as wide in azimuth and 1/10th as wide in elevation).
** In the absence of any other objects/reflections, the other antenna would only receive the power that was directly radiate towards it, so it really doesn't matter what the gain in any other direction is. Though, in reality, even with ground bounces you can get some screwy interference patterns.
Final thought -- if you look at a free space path loss calculator, e.g. https://www.pasternack.com/t-calculator-fspl.aspx, that 2.2 dBi gain gives you about a 22 m additional range (same pathloss at 78 m for a 0 dBi antenna as 100 m for a 2.2 dBi antenna). Your 7 dBi antenna would give another 75 m, up to 175 m for the same pathloss. Again, this is only in an ideal freespace (no reflections/absorption) and a perfectly pointed antenna.
You should also note that you can be breaking the law with too high a gain of antenna -- the FCC limits unlicensed transmission in the 2.4 GHz band to 1 watt EIRP (equivalent isotropic radiated power). Also, at some distance the bluetooth protocol will probably actually start to fail, as the latency from speed of light (about 1 us roundtrip at 175 m) can break things (though I'm much more familiar with WiFi).