Estimation of Amplitude, Frequency and Phase of Linear Combination of Harmonic Signal Beyond the Leakage Resolution of DFT
Solving the Linear Combination of Real Harmonic Signal
The data model is given by:
$$ x \left( t \right) = \sum_{i = 1}^{M} {a}_{i} \sin \left( 2 \pi {f}_{i} t + {\phi}_{i} \right) + n \left( t \right) $$
Where $ M, {\left\{ {a}_{i} \right\}}_{i = 1}^{M}, {\left\{ {f}_{i} \right\}}_{i = 1}^{M}, {\left\{ {\phi}_{i} \right\}}_{i = 1}^{M} $ are unknown parameters and $ n \left( t \right) $ is Additive Gaussian White Noise (AWGN).

Estimating the parameters above requires 4 steps solution:

Estimate the model order ($ M $) / number of signals.
Estimate the frequencies accurately using direct method (Given the number of frequencies).
Estimate the amplitude and phase of the model given the frequencies (Usually using Non Linear Least Squares solver).
Estimate all amplitudes, frequencies and phase (Usually using Non Linear Least Squares solver).

The above works only in very very high SNR cases. For low SNR this problem is probably unsolvable (Certainly for large $ M $).
If the frequencies are well spread (Far from each other) then steps (1) and (2) can be achieved using DFT (fft()).
Yet in case the frequencies are close in the best case the estimation of the frequency won't be accurate (Leakage from near by frequencies will shift the peak) and in the worse the case frequencies will be blended and neither the number of signals nor the frequencies is achievable.

In the images above I used observation time of 12 [Sec] with 4 signals with frequencies of [0.95; 1.00; 1.05; 1.10] [Hz]. Since I took 1 / 10 of observation time in your question, it is equivalent of frequencies being 0.005 far apart in the 120 [Sec] observation time. I just wanted to deal with less samples.
As can be seen in the image above, in the DFT there is no way estimating the number of signals and certainly extracting the frequencies.
But using Super Resolution methods one could solve this case!
See some information about Frequency Domain Super Resolution in the section below.
Yet for this case I used different method for Super Resolution which I can't reveal (Used commercially by me as an advisor).
I also developed a method to estimate the number of signals.
In the case above indeed my method estimated 4 signals and the estimated frequencies were [0.9503, 1.0016, 1.0483, 1.0996] [Hz].
Then applying the next 2 steps I could even farther improve results:

As can be seen from above, the estimated signal is almost perfectly aligned with the ground truth (The model with known parameters with no noise).
Indeed the SNR here is very high yet still, without the Super Resolution method, it wouldn't work.
The full code is available on my StackExchange Signal Processing Q74024 GitHub Repository.
Unfortunately, I can't disclose the code of the estimation of the number of parameters and the Super Resolution.
Frequency Domain Super Resolution
Old non modern methods will use some Windowing tricks which falls short in most cases.
What you really need is Super Resolution. Super Resolution basically is equivalent to a &quot;Window Method&quot; with very narrow main lobe and almost no side lobes.
You can employ Compressed Sensing / Sparse Representation for Super Resolution in Frequency Domain.
One way to do so is solving the problem:
$$ \arg \min_{\boldsymbol{x}} \frac{1}{2} {\left\| F \boldsymbol{x} - \boldsymbol{y} \right\|}_{2}^{2} + \lambda {\left\| \boldsymbol{x} \right\|}_{1} $$
Super Resolution means, in that context, being able to resolve frequencies which are closer than what the observation time suggests (overcoming Leakage issues):

In the above you can see the DFT of a sum of 2 sines with the given frequencies. The Gaussian model is using $ {L}_{2} $ for regularization (Which is basically damped zero padding).
You may see that the $ {L}_{1} $ could resolve the 2 sines even when they are only 0.5 [Hz] apart with an observation windows of 1 [Sec].
The answer was taken from my answer for Super Resolution in Frequency Domain Using Compressed Sensing.