I personally [if I were i) the 'corresponding author', ii) the senior author, iii) the principal investigator, etc.] would NOT have done / committed such a breach of confidence ("without informing AND / OR consent of the first author"). Normally the first author is not 'a student' (in former times it may have occured that 'student slaves' working hard in a research project team were given the opportunity to appear as first authors - just saying) - and the Corresponding Author isn't 'God' (hopefully). The "order" as well as the 'number' of authors / coauthors of a scientific article to be published usually is determined in group discussion or by writing to ALL (co-)authors and then settled in the / a manuscript to be submitted to the Editorial Office of a Journal or a Publishing company (if the contribution were, e.g., a chapter in a book). Usually entitling a researcher to act as a "first author" will not be 'bread-crumb' distribution ... therefore most publishers request description of the scope of activity /-ies the author / authors has / have contributed to the whole work / publication (as also most serious publishers would request a 'confirmation' by any of the involved author(s) / co-author(s) that they have 'authored' / authorized the publication of a manuscript as is / was submitted. Therefore, CHANGING authorship, or - as asked in your request - ADDING (an)other co-author(s) to an already submitted and accepted Manuscript intended to be published a.s.a.p., USUALLY CANNOT be done without 'certified' = written consent of ALL authors... My humble and honest opinion though....

The corresponding author has no right to add, delete or change the position of authors without consulting the other authors. Normally the authors once fixed should not be changed

Most journals have guidelines on authorship. Here is a link on authorship guidelines from Taylor & Francis about roles, definitions, and change of authors.

https://authorservices.taylorandfrancis.com/editorial-policies/defining-authorship-research-paper/

I suppose if a journal has no such guidelines, it doesn't matter what anyone does. However, I would not want to publish in a journal if not peer-reviewed and if it exists without authorship guidelines.