It seems that it's not possible to add hoverinfo to shapes directly. But you can obtain something very close to what seems to be the desired effect through the right combination of shapes and traces. The following plot is made from specifying two rectangles in a list like:
shapes = [[2,6,2,6],
[4,7,4,7]]
The rest of the code snippet is set up to be flexible with regards to the number of shapes, and the colors assigned to them and the corresponding traces to make that little dot in the lower right corners of the shapes.
Plot:

If this is something you can use, we can discuss ways to edit what is being displayed in the hoverinfo.
Complete code:
# Imports
import pandas as pd
#import matplotlib.pyplot as plt
import numpy as np
import plotly.graph_objects as go
import plotly.express as px
# shape definitions
shapes = [[2,6,2,6],
[4,7,4,7]]
# color management
# define colors as a list
colors = px.colors.qualitative.Plotly
# convert plotly hex colors to rgba to enable transparency adjustments
def hex_rgba(hex, transparency):
col_hex = hex.lstrip('#')
col_rgb = list(int(col_hex[i:i+2], 16) for i in (0, 2, 4))
col_rgb.extend([transparency])
areacol = tuple(col_rgb)
return areacol
rgba = [hex_rgba(c, transparency=0.4) for c in colors]
colCycle = ['rgba'+str(elem) for elem in rgba]
# plotly setup
fig = go.Figure()
# shapes
for i, s in enumerate(shapes):
fig.add_shape(dict(type="rect",
x0=s[0],
y0=s[2],
x1=s[1],
y1=s[3],
layer='above',
fillcolor=colCycle[i],
line=dict(
color=colors[i],
width=3)))
# traces as dots in the lower right corner for each shape
for i, s in enumerate(shapes):
fig.add_trace(go.Scatter(x=[s[1]], y=[s[2]], name = "Hoverinfo " +str(i + 1),
showlegend=False,
mode='markers', marker=dict(color = colors[i], size=12)))
# edit layout
fig.update_layout(yaxis=dict(range=[0,8], showgrid=True),
xaxis=dict(range=[0,8], showgrid=True))
fig.show()