Your manager's role is to oversee the workings of the department (or entire company). How she handled the problem only caused friction between you resulting in a difficult, working relationship.
No analytic professional, a transition and the catastrophic Covid pandemic. All combined will mean some risky decisions need to be taken.
That's business - and you made a decision because you thought it was in the client's (and company's) best interest.
However. It went wrong - and unfortunately, the client may focus on the mistake and any attempt at justifying the decision will be viewed as an excuse.
More pressure for your new manager and the risk of the client taking their business elsewhere.
Let's be fair. It's understandable and she was right in telling you.
There could have been a better way to handle it.
Your new manager appears to shy away from confrontation. The emails are her way of taking that chance you'll agree with her, yet at the same time saving her the aggravation of having to confront you.
She's hoping this will solve the problem and assume everybody will simply move forward.
Of course. It's not always the case.
There's a risk of creating a hostile work environment.
Take a step back to appreciate what is really happening.
The new manager has good intentions - but lacking that ability to convey this.
Accept it's early days as she may be new to this level of management herself.
Managers are supposed to 'troubleshoot', give guidance, positive leadership and help oversee the workings of a department or even a whole company.
However. It often doesn't work that way because many new managers find themselves undertaking a role that is more responsibility than they imagined. The result. The manager being the cause - rather than the solution - to many problems.
People often undertake the role of manager/team leader with great initial enthusiasm. Then within a few days wake up to the realisation of what they have taken on.
Managers can have brilliant minds and enter the profession from various routes, yet tend to share a popular trait. They often don't appreciate what's really involved in order to do a particular job.
Some managers enter the profession via their own company being taken over and find it hard going from being 'their own boss' to becoming a part of a larger organisation.
There are those that enter management straight from university. Reading the text books and writing out that dissertation are one thing. When it comes to managing a department/company it's a totally different learning curve.
Then there are those who become managers because their relatives hold a directorship role within the company - such as owning it. They take on the role immediately after college or university, without even studying business.
They try to organise the company in order to please the most important people in their lives without giving focus to the real workings and 'behind the scenes' of the office/factory floor.
Some managers enter the role after working for many years 'on the shop floor' and find the role can be thankless and unbearable. It's often assumed that by taking on the management role, there'll be a bigger financial reward, more 'company perks' and perhaps even more respect.
Sadly. The stress of the role, the conflict with former workmates and being accused of spending too long away from the tools can make the job difficult.
It's no wonder many employees would rather pass over the opportunity.
Many companies - such as yours - find it more productive to introduce a new manager 'from the outside' rather than appoint someone who is already working for the company.
This is in the hope of bringing in fresh perspectives from their leadership and can help to neutralise any disagreements or conflict because there's less risk of things getting too personal.
This is because the new manager is not familiar with the workforce and can feel more comfortable implementing new strategies. This appears to be the case in your organisation.
Trying to put all of this simply, you're in a difficult situation. The anger isn't going to help.
Accept the situation for what it is. It's a business.
Take some positive action to help your working day run smoothly. Let's be fair. The working day is long - especially with conflict.
In business, bear in mind we are all professionals.
Starting with your first admonition. Both you and your colleague took it upon yourselves to try and rectify a clients problem. You showed initiative and your intentions were good.
However. The manager showed a lack of assertive leadership skills.
Next time....
Discuss the incident with your new manager and state that your primary concern was for the client and their continued business.
Follow on to say that you thought it unfair to be chastised via email when you were only trying your best to solve the client's problem.
Mention your 'client strategy'.
Managers love new ideas - especially when they feel that they have contributed.
Do make suggestions and raise issues but in a way as to engage with the manager. Encourage the manager to feel they have been a serious part of the new strategy.
Some managers like to 'think about' an idea for a while, then take some of the credit for implementing their colleagues ideas.
In such a scenario, just compliment the manager for using the idea and 'good team thinking'. It's difficult but just the way things are at times.
When you have a 'one-to-one' with your manager, point out (carefully) that her emails have caused some offence to your colleagues and there's a risk of it causing friction.
A common problem is being unable to 'switch off' at the end of the day. You are currently 'taking work home'.
Read a book or two about stress management and remember that worrying about work after the shift is over will not help. Nobody will thank you for it.
The test with a 'trick question'....Is this test relevant to your job?....Would your work performance be a more reliable indicator of your knowledge?......Worth asking.
It looks like you're going through a tough time.
However. Don't leave just yet. See how things go - because the next few months will be hard for all companies.
Give yourself some time to plan ahead and decide if you want to find another job.
Do some reading on management techniques to gain an insight into the workings of management.
Further reading on self-assertiveness may help as well.
This may help you to deal with your difficult new manager.
The working day can be long and beset with many problems, including what appears to be a manager causing trouble (even if unintentionally).
However. At the end of the day, we are all at work for one reason - to earn a living.