So you want to reconcile, or try to at least. Fine, no trouble with that decision even if it's a little early perhaps. So let's start there and mention a few things:
Her words of affirmation toward you sound good and are a positive start.
Going to counseling to figure out her thoughts, feelings and it sounds like... temptations is good too. However, this one comes with a big caution. NOT ALL COUNSELORS are created equal. Not in skill and not in outlook. Get someone experienced with infidelity and with trying to help people both find out why they cheated and how to remedy it so they can repair the marriage. You don't want a counselor who will help her "find herself' and advocate non monogamous relationship or any of those paths.
She needs to understand how dopamine lures people into temptation and acts like a powerful drug. It creates fantasies where people feel dissatisfied with what they have and desire for others. This is important because it sounds like she is questioning marriage despite saying she loves you. That's a dangerous space if you want to R. Here is where reading the right books and a skilled counselor with infidelity experience can help her see through these issues. You might consider this forum on the wayward side for her because there are former waywards here who are amazing in helping people see these dynamics for what they are, an illusion based usually upon some mixture of need for validation and dopamine fueled behavior.
Get the book Not Just Friends by Shirley Glass and maybe another book recommended here at SI. That way she can read solid work on infidelity and not some BS that will confuse her more.... there is a lot of BS out on the internet that will not help.
Does she have friends who were aware of the A and encouraging her? Those relationships are not safe for your marriage. She needs the opposite, a friend who will tell her to take her head out of her ass and repair the marriage. Those people are worth their weight in gold right now.
Just because you have decided to try to reconcile does not mean it is ok to do the pick me dance. It will work against you. It is ok to be pissed, hurt, devastated, frustrated etc. It is ok for her to see all those things and realize she created them. Does she realize how you feel? Does she know the marriage is hanging by a thread even if you want to try to R? She needs to understand what she did and the impact, asap, and your remarks don't quite show us she gets that yet. It appears that you may be doing the pick me dance to some degree. You haven't given much data for us to digest but any betrayed spouse who decides for R right away is usually doing it at least a little bit I think.
She should not be going to the same gym anymore. If she is, she will be in contact. I think she was head over heels for this guy. 1800 texts, sex... yeah she is on a dopamine high almost certainly and you need lots of cold water to help her out of it. No contact gets promised often but broken almost as often. Have you put your foot down on this? You need to. She needs to know you wont share your wife and this is where seeing a D lawyer even though you want R may help you quite a bit. She needs time because she is head over heels and doesn't understand how she could be when she loves you. All steps should be taken PROACTIVELY to end the affair. Dont think it is enough to give her space so she can figure it out. Sure, she may need space but she needs to understand you are not chasing her. You're married, not pursuing her. The other guy is pursuing her, If contact continues then you are still in infidelity.
Is the AP married or does he have a gf? If so, you should tell the other woman. It will pour the cold light of day on the affair and take away the fantasy. It almost always helps to end the affair.
You love her and want to stay married. The best way to have a chance for her to want the same thing is for you to be firm, get out of infidelity and take most of the great steps being offered by the collective wisdom here at SI. They will help you avoid the pick me dance, which helps her out of her dopamine fueled fantasy. Be assertive. Be strong. Contend with the idea that you may have to D even though you want R and let her know that everything is potentially on the table. And it largely depends on her actions from here on out.