What does and doesn't work in math education is an empirical question. For instance, how math is taught in Singapore means what works for those students may be different than how math works and what is taught in Chicago. So I'd push back on any inclination that education needs to be this or that way when it comes to notation.
I think the best approach might be to explain the difference between arithmetic equality, logical equivalence (either with three lines or bidirectional arrow) all of which are equivalence relations. Thus, to use either of these is to emphasize the equivalence relation, which entails reflexivity, symmetry, and transitivity. To use the material conditional either as an 'if-then' or 'because' construction in natural language emphasizes logical consequence. So, when you're teaching solving for unknowns, I'd start with logical consequence and then move to explaining how the bi-conditional constitutes identity. And, like this post, I'd do in plain, natural language.
Part of the difference in how you approach this is a function of the level of sophistication of the student. A really bright student will hear this once or twice and understand, whereas someone who struggles may be confused by the distinctions in symbols since they've never likely been explained this. Certainly not at the elementary level, probably not at the secondary level, and probably poorly at the higher educational level. The use of the material conditional, for me, is superior because it emphasizes process, rather than entity. An arrow means intuitively, start here and end there, and with each use, one can talk about why we move from the initial to final state. With the equals symbol, it may be a little more mysterious why the statement changes. To really aid a student, you can write a brief reason above the left-to-right arrow. For instance, if you have substituted a constant value into a variable, simply mark "SUB x" over the arrow. If you have have changed the order of an addend and adder, you simply write "COMM ADD" to say you have invoked the commutativity of addition as your justification.
In this way, much like a two-column proof where a rationale is provided, but less tabular in form, you can layout the concepts behind the symbolism. One of the chief problems with poor math education is an over-use of symbols and an under-use of natural language to explain. Thus, there are hordes of students who can manipulate symbols successfully, and have no semantic grounding, and hence no real understanding of why they do what they do.
So, no matter what symbols you use, just ensure students understand why.
⟺sidestepping confusion about extraneous solutions? In any case, I have a response at Is
⟹the best symbol when rewriting equations?, I prefer to reserve
≡for identities and equivalence relations because nonstandard/frivolous usage of symbols is jarring, and I agree with @guest about omitting all connective symbols, especially if they be overloading