I would highlight points of interest with fig.add_trace(go.Scatterternary() and tweak the text amd marker attributes to make it look good. Here's an example where I've highlighted a point in the lower left corner:
Plot 2

Why not fig.add_annotatoins() or something else?
The perfect would arguably be to be able just set the hoverinfo for any given marker to show all the time. But to my knowledge that's just not possible at the moment. You could also use fig.add_annotations(), but as far as I know you would have to rely on x, y coordinates only both xref and yref set to paper.
An upside of the fig.add_trace(go.Scatterternary() though is that you can include those data in the legend as well with:
fig.update_layout(showlegend = True)
fig.for_each_trace(lambda t: t.update(showlegend = False))
fig.data[-1].showlegend = True
Plot 2

Complete code:
import plotly.figure_factory as ff
import numpy as np
import plotly.graph_objects as go
Al, Cu = np.mgrid[0:1:7j, 0:1:7j]
Al, Cu = Al.ravel(), Cu.ravel()
mask = Al + Cu <= 1
Al, Cu = Al[mask], Cu[mask]
Y = 1 - Al - Cu
enthalpy = (Al - 0.5) * (Cu - 0.5) * (Y - 1)**2
fig = ff.create_ternary_contour(np.array([Al, Y, Cu]), enthalpy,
pole_labels=['Al', 'Y', 'Cu'],
ncontours=20,
coloring='lines',
showmarkers=True)
fig.add_trace(go.Scatterternary(
a = [2],
b = [8],
c = [2],
mode = "markers+text",
text = ["A"],
texttemplate = "%{text}<br>(%{a:.2f}, %{b:.2f}, %{c:.2f})",
textposition = "bottom center",
marker_symbol = 'circle-open',
marker_color = 'green',
marker_line_width = 3,
marker_size = 12,
textfont = {'family': "Times", 'size': [14, 14, 14],
# 'color': ["IndianRed", "MediumPurple", "DarkOrange"]
}
))
fig.update_layout(showlegend = True)
fig.for_each_trace(lambda t: t.update(showlegend = False))
fig.data[-1].showlegend = True
fig.show()