Should I tell my boss about a job offer with a substantial pay raise that I never intended to accept?

I'll try my hardest to keep this concise, but I have a feeling it will be a bit convoluted.

I have been at my job for exactly one year this week (but who is counting). A quick background, I graduated with my MBA in December 2020 in an attempt to pivot away from my original career path. I took this job because it was genuinely a way off of the sinking ship that was my last company, and because it provided me with potential for career growth that would better utilize my MBA (plus a 16% raise on what I was making at the last job). The CEO and my boss (who was recently promoted to the COO) both expressed that they have long-term goals for me, but this has been pretty nebulous in terms of what I would do and when it would happen. So essentially I'm just hanging out at this job which is in my previous career path (that also utilizes my MBA a little bit) for an unknown amount of time.

I was recently contacted by a LinkedIn headhunter who plugged me in with an opportunity that I interviewed for, and they want to hire me and give me a 14% raise on my current salary. I never actually intended on taking this job, I know the company and its just bad news all around - the only reason I entertained the option was the money to feel out my worth, but deep down I was not going to accept it.

I like my boss, she likes the work that I do. I recently approached her prior to my one year anniversary and I wrote out my formal plan for my department moving forward, which included a bullet point that involved me hiring a second-in-command so that I can move on to bigger things in the company. I told her that my department plan was just a formality, but I never once mentioned a raise. I just told her I want to eventually feel like I have an MBA. Problem with my field is that its super difficult to get any kind of metrics that show that you improved the department - in my field, if nothing bad happens, then you're doing a good job. Regardless, I built the department from the ground up and its now in fantastic shape.

Now that I tested the market and found where another company values me at, it changed things for me. I know my company is doing very well, but they have made several adjustments recently out of budget concerns, so I don't think they would give me much of a raise, if any. I want to approach her and tell her that I received a job offer and tell her the proposed salary, and I want to tell her that I'm declining it because I genuinely love working for this company and that I am committed to my work here. But I wanted to be transparent with her with the types of things that are coming to me (as opposed to me searching for them). The purpose of me telling her this is to build trust with her and the company and also to express that I feel like I may be undervalued.

The other honest truth is that I have been gently testing the market for other jobs that are more in line with my career change - the only way I would accept a job is if its a promotion in terms of career growth, the company/role is good, and the money is good - it may be months or years before I come up with an offer that is that tempting. This recent offer only checks one of the boxes, but not the other two. But I won't tell her that part.

Thoughts?

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