This approach could reduce your overall security in certain cases, not improve it.
Information Security consists of three attributes: Confidentiality, Integrity, and Availability (the CIA triad). By focusing exclusively on one, you can easily overlook the importance of the others.
Confidentiality of passwords is achieved through the principles of entropy: how 'unguessable' is your password? This is commonly measured by the size of the brute force guessing space, expressed in terms of powers of 2 or bits. A brute force attacker has only so much capacity to guess; by selecting a longer password to increase this entropy you can exceed any known or predicted capability to guess. Getting the entropy over 80 bits (or pick your value) will put the password out of reach of even nation state actors. Regardless of the overly simplified description above, the point is that going above and beyond whatever "out of reach" is doesn't significantly add to your security. And it isn't relevant to security if you achieve the desired entropy by using 10 Unicode characters or 17 ASCII characters.
Availability means "can I get to my data when I need it?" If you use full Unicode character sets, you risk running afoul of various sites that don't support Unicode, or browsers or OSes that implement Unicode incorrectly, or sites that invisibly translate Unicode to ASCII under the covers. The resulting confusion increases the risk of restricting your future access to the data. This represents a potential decrease in future Availability.
In general, the likelihood of an attacker brute forcing your 80 bit password is not nearly as high as the likelihood of encountering a poorly coded site that doesn't handle Unicode properly. Therefore your overall security could be decreased instead of increased.
Of course, many sites have password length and other restrictions that dramatically limit the entropy of your passwords, too. In those cases, using the full Unicode set may increase the entropy of your passwords, assuming they don't have other hidden flaws. So on those sites, you may be improving your security; but it's virtually impossible to tell from outside if a site is properly handling your password data.