Is it normal that journals strongly suggest a professional English editing service?
In one journal where I am familiar with the editorial workflow, the review form explicitly asks reviewers to rate the language quality of the manuscript. Based on this rating, the editor can tick an item similar to "Needs language revisions" when putting together the decision letter. The decision letter will then contain a paragraph that advises the authors to do a language revision. I am not sure at the moment whether a particular service is being recommended there.
The point is that such a recommendation can get into the letter easily, but will not be included by default. Probably the editor only wrote the first two or three sentences of the letter, maybe without thinking carefully about the exact formulation, and the rest is based on a customizable template. Nevertheless, it usually means that at least one reviewer was criticizing language usage, maybe even without giving specific comments on it. I would advise you to at least double-check on language usage, and if possible have it proof-read by someone else with very good English skills or a native speaker.
However, as long as the reviewers can understand the technical content well, these points are usually not decisive for the acceptance of the manuscript. Especially, as long as any language problems are corrected, I can't imagine that the editor will care whether you use the suggested language service or not.
No, this is not normal. I have never received such a suggestion despite the fact that neither I nor any of my co-authors were native speakers of English, and there was no reason (such as name or affiliation) for any editor to assume this. I also never heard of anybody else receiving such a suggestion (which does not mean much, however). In particular, I did not receive such a suggestion when publishing with the same publisher (AIP).
Moreover, the first paragraph of your example mail does not seem to be an automatically generated or canned text block to me. Such text blocks are usually more diplomatic and would not contain words such as awkward. (The rest of the mail seems to be a prepared text block, however.)
Normal or not (and it's abnormal), this practice is problematic because it's unclear if the editor has vested interest to recommend this particular editing service. There are many professional editing services, why just Edanz? If there is any agreement between the journals and Edanz in the form of a commission or kick-back, then I will not trust the judgment of the editor on my written English, as he/she will be inclined to be more stringent or even unreasonably stringent.
Moving forward, if that "awkward" troubles you, it may be advisable to seek help from a professional editor who is not related to Edanz. While many comments here praise your English, writing a question and writing a manuscript are of two different leagues and there could be grammatically correct but unconventional expressions in your work, so don't take those praises as a proof that your paper does not need to be edited. Meeting with an editor allows you to get a general scope of the problems, if any, and also provides an excellent chance to evaluate your overall English usage. When replying the editor, you may also indicate that you have sought help from a third party editor to edit your work.
Good luck.